Check: if the value is 13, then adding the 7 back gives 20, and 20 \div 4 = 5, which is the x we were given ✓
Tip: never write the number right next to the coefficient. 4x with x = 5 is 4 \times 5, not "45". Writing 4(5) with parentheses makes the multiplication clear.
Question 2 of 36
No calculatorFill in
Evaluate 3a + 2b when a = 4 and b = -5.
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Substitute both values in parentheses. What is 2 \times (-5)?
Step-by-step solution
Substitute both values: 3(4) + 2(-5).
Multiply: 3(4) = 12 and 2(-5) = -10.
Add: 12 + (-10) = 12 - 10 = 2.
The value is 2.
Check: on the calculator: 3×4+2×((−)5)enter gives 2 ✓
Tip: a positive times a negative is negative. Adding a negative number is the same as subtracting its size: 12 + (-10) = 12 - 10. Substituting b without parentheses (2 - 5) is how the common wrong answer 9 appears.
Question 3 of 36
No calculator
What is the value of -2x + 9 when x = -3?
Hint
Write -2(-3) + 9. What is a negative times a negative?
Step-by-step solution
Substitute in parentheses: -2(-3) + 9.
Multiply: (-2)(-3) = 6, because a negative times a negative is positive.
Add: 6 + 9 = 15.
The value is 15.
Check: on the calculator: (−)2×((−)3)+9enter gives 15 ✓
Tip: multiply before you add. The expression -2x + 9 does not mean -2(x + 9); the 9 is added only after -2x has been found. Putting -3 in parentheses, -2(-3), makes the sign rule easy to see.
Question 4 of 36
No calculator
If k = 7, what number does the expression 9 + 6k equal?
Hint
6k means 6 \times k. Do the multiplication before the addition.
Step-by-step solution
Replace k with 7, using parentheses: 9 + 6(7).
Multiply first: 6 \times 7 = 42.
Then add: 9 + 42 = 51.
The value is 51. Writing 6(7) with parentheses keeps you from reading 6k as the two-digit number 67.
Check: work backwards: 51 - 9 = 42 and 42 \div 6 = 7, which is the value of k ✓
Tip: order of operations is not "left to right". Multiplication comes before addition even when the addition is written first.
Question 5 of 36
No calculatorFill in
Evaluate 12 - 2n when n = 4.5.
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Multiply 2 \times 4.5 first, then subtract from 12.
Step-by-step solution
Substitute: 12 - 2(4.5).
Multiply first: 2 \times 4.5 = 9.
Subtract: 12 - 9 = 3.
The value is 3.
Check: work backwards: if 12 - 2n = 3, then 2n = 9 and n = 4.5 ✓
Tip: doubling a number that ends in .5 always gives a whole number (2 \times 4.5 = 9). Spotting that lets you skip the calculator. A common slip is 12 - 2 = 10 first, then 10 \times 4.5 = 45 - that breaks the order of operations.
Question 6 of 36
No calculatorHot spot
Click the point on the number line that shows the value of 5 - 2x when x = 4.
Click on the figure to mark your answer (or focus it and use the arrow keys).
Hint
Find 2 \times 4 first. Then subtract that from 5. Can the answer be negative?
Step-by-step solution
Substitute: 5 - 2(4).
Multiply first: 2 \times 4 = 8.
Subtract: 5 - 8 = -3.
On the number line, -3 is 3 units to the left of 0.
The point to click is -3.
Check:-3 means you started at 5 and moved 8 to the left: 5 \to 0 is 5 steps, and 3 more steps reach -3 ✓
Tip: when you subtract a bigger number from a smaller one, the result is negative. A common slip is 8 - 5 = 3 (subtracting in the wrong order), which lands on the wrong side of 0.
Question 7 of 36
No calculator
What is the value of 5p - 3q when p = -2 and q = -4?
Hint
Put each value in parentheses: 5(-2) - 3(-4). Work out each product before subtracting.
Step-by-step solution
Substitute with parentheses: 5(-2) - 3(-4).
First product: 5(-2) = -10.
Second product: 3(-4) = -12, and subtracting -12 means adding 12.
Combine: -10 + 12 = 2.
The value is 2.
Check: think of it as -10 - (-12). Subtracting a negative is adding the positive: -10 + 12 = 2 ✓
Tip: you can also read -3q as (-3)(q): (-3)(-4) = +12. Either way, two negatives multiply to a positive.
Question 8 of 36
A plumber charges a $60 service fee plus $45 per hour. The total charge in dollars for h hours is 45h + 60.
What is the total charge for a job that takes 3.5 hours?
Hint
Multiply the hourly rate by the hours first, then add the fee.
Step-by-step solution
Substitute h = 3.5: 45(3.5) + 60.
Multiply first: 45 \times 3.5 = 157.5.
Add the fee: 157.5 + 60 = 217.5.
The total charge is $217.50.
Check: 3 hours cost 3 \times 45 = 135 dollars and half an hour costs 22.50 dollars, so labor is 157.50 dollars. Add the 60-dollar fee: 217.50 dollars ✓
Tip: the fee is charged once; only the hourly rate is multiplied by the hours. That is exactly what the order of operations does with 45h + 60.
Question 9 of 36
Fill in
Evaluate the expression when x = 6 and y = -3.
\frac{3x - 2y}{4}
Type your answer in the box. Fractions like 3/4 are fine.
Hint
The fraction bar is a grouping symbol: work out the entire numerator before dividing by 4.
Step-by-step solution
Substitute: \dfrac{3(6) - 2(-3)}{4}.
Multiply in the numerator: 3(6) = 18 and 2(-3) = -6.
Subtract: 18 - (-6) = 18 + 6 = 24.
Divide: 24 \div 4 = 6.
The value is 6.
Check: on the calculator, type (3×6−2×((−)3))÷4enter → 6 ✓
Tip: subtracting a negative is adding. Common wrong answers here are 3 (from 18 - 6 = 12, then 12 \div 4) and 19.5 (from dividing only the last term by 4: 18 - \tfrac{-6}{4} = 18 + 1.5).
Question 10 of 36
The formula F = 1.8C + 32 converts a temperature in degrees Celsius (C) to degrees Fahrenheit (F).
What is -15°C in degrees Fahrenheit?
Hint
Multiply 1.8 by -15 first. Then add 32 to that negative number.
Step-by-step solution
Substitute: F = 1.8(-15) + 32.
Multiply: 1.8 \times (-15) = -27.
Add: -27 + 32 = 5.
So -15°C equals 5°F.
Check: work backwards: 5 - 32 = -27, and -27 \div 1.8 = -15 ✓
Tip: when you add a positive number to a negative number, subtract the smaller size from the larger, 32 - 27 = 5, and keep the sign of the larger one (here 32, positive). A temperature below 0°C can still be above 0°F, so a small positive answer is reasonable.
Question 11 of 36
Drop-down
Select the value that makes the statement true.
When x = -4, the value of 7 - 3x is .
Choose an answer from each menu.
Hint
Find 3x first, then subtract it from 7. Subtracting a negative number means adding.
Step-by-step solution
Substitute: 7 - 3(-4).
Multiply first: 3(-4) = -12.
Subtract: 7 - (-12) = 7 + 12 = 19.
The value is 19.
Check: think of it as 7 + (-3)(-4) = 7 + 12 = 19 ✓. On the calculator: 7−3×((−)4)enter gives 19 ✓
Tip: you can read 7 - 3x as 7 + (-3)x. Then (-3)(-4) = +12, and the sign error disappears. Also remember that multiplication comes before subtraction, so never compute 7 - 3 first.
Question 12 of 36
A moving-truck rental costs $29.95 plus $0.79 per mile. The cost in dollars for m miles is 29.95 + 0.79m.
What is the cost of renting the truck and driving it 120 miles?
Hint
Find the mileage charge 0.79 \times 120 first, then add the base price.
Step-by-step solution
Substitute m = 120: 29.95 + 0.79(120).
Multiply first: 0.79 \times 120 = 94.80.
Add the base price: 29.95 + 94.80 = 124.75.
The rental costs $124.75.
Check: estimate first: 0.79 is about 0.80, and 0.80 \times 120 = 96. Adding about 30 gives about 126, which is close to 124.75 ✓
Tip: even when the constant is written first, as in 29.95 + 0.79m, the multiplication is still done before the addition.
Question 13 of 36
Select all
Select all expressions that have a value of 10 when x = -2.
Select all that apply.
Hint
Evaluate each expression separately with x = -2 in parentheses.
Step-by-step solution
Substitute x = -2 into each expression:
-5x = -5(-2) = 10 ✓
4 - 3x = 4 - 3(-2) = 4 + 6 = 10 ✓
2x + 6 = 2(-2) + 6 = -4 + 6 = 2 ✗
14 + 2x = 14 + 2(-2) = 14 - 4 = 10 ✓
-2x + 14 = -2(-2) + 14 = 4 + 14 = 18 ✗
The expressions with value 10 are -5x, 4 - 3x and 14 + 2x.
Check: the two wrong ones give 10 only with a sign error: 2(2) + 6 = 10 uses x = 2, and -4 + 14 = 10 uses (-2)(-2) = -4.
Tip: in "select all" questions, test every choice. Do not stop after finding one that works.
Question 14 of 36
A car-rental company offers two plans. The cost, in dollars, to drive m miles is:
Plan
Cost
Plan A
25 + 0.15m
Plan B
10 + 0.25m
Which statement is true for a trip of 120 miles?
Hint
Evaluate both expressions at m = 120. Then subtract.
Step-by-step solution
Plan A: 25 + 0.15(120) = 25 + 18 = 43 dollars.
Plan B: 10 + 0.25(120) = 10 + 30 = 40 dollars.
Compare: 43 - 40 = 3, so Plan B is cheaper by $3.
The true statement is Plan B costs $3 less than Plan A.
Check:0.15 \times 120: 10% of 120 is 12 and 5% is 6, so 18 ✓. 0.25 \times 120 is a quarter of 120, which is 30 ✓
Tip: a lower fixed fee does not always mean a lower total, and neither does a lower rate. On the GED, always evaluate both plans at the given input.
Question 15 of 36
Fill in
Complete the table of values for the expression 4x - 3.
x
-2
0
2.5
4x - 3
-3
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Substitute each x in parentheses. For x = -2, what is 4(-2)?
Step-by-step solution
For x = -2: 4(-2) - 3 = -8 - 3 = -11.
For x = 0 (given): 4(0) - 3 = -3. This confirms how the table works.
For x = 2.5: 4(2.5) - 3 = 10 - 3 = 7.
The missing values are -11 and 7.
Check: the values should go up by 4 for every 1 that x goes up. From x = -2 to x = 0 is 2 steps: -11 + 8 = -3 ✓. From x = 0 to x = 2.5 is 2.5 steps: -3 + 10 = 7 ✓
Tip: in a table of a linear expression, equal steps in x give equal steps in the value. Use that pattern to check your work.
Question 16 of 36
What is the value of the expression below when x = 4?
\frac{20 - 2x}{x + 1}
Hint
The fraction bar works like parentheses: find the whole top and the whole bottom first, then divide.
Step-by-step solution
Top: 20 - 2(4) = 20 - 8 = 12.
Bottom: 4 + 1 = 5.
Divide: \dfrac{12}{5} = 2.4.
The value is 2.4.
Check:2.4 \times 5 = 12 ✓, and 12 is the top when x = 4.
Why not 18.4 or 4? Those come from dividing only part of the expression. The bar divides everything above it by everything below it.
Tip: you can type it on the TI-30XS as (20 − 2 × 4) ÷ (4 + 1). Without the parentheses the calculator divides only part of the expression.
Question 17 of 36
Drop-down
A caterer charges a $125 setup fee plus $18.50 per guest. The total charge, in dollars, for g guests is 125 + 18.5g.
Select the amount that makes the statement true.
The total charge for 64 guests is .
Choose an answer from each menu.
Hint
Multiply the per-guest price by the number of guests first. Then add the setup fee once.
Step-by-step solution
Substitute g = 64: 125 + 18.5(64).
Multiply first: 18.5 \times 64 = 1{,}184.
Add the setup fee: 125 + 1{,}184 = 1{,}309.
The total charge is $1,309.
Check: estimate: about \$20 \times 64 = \$1{,}280, minus a little, plus \$125 is roughly \$1{,}300 ✓
Tip: a fixed fee is paid once, no matter how many guests come; only the per-guest price is multiplied by g. Adding 125 and 18.5 first would charge the setup fee to every guest.
Question 18 of 36
The formula C = \tfrac{5}{9}(F - 32) converts a temperature in degrees Fahrenheit (F) to degrees Celsius (C).
What is 14°F in degrees Celsius?
Hint
Work inside the parentheses first. Is 14 - 32 positive or negative?
Check: convert back with F = 1.8C + 32: 1.8(-10) + 32 = -18 + 32 = 14 ✓
Tip: temperatures below 32°F are below freezing, so they must come out below 0 in Celsius. That fact alone rules out positive answers here.
Question 19 of 36
Select all
Suppose a = -2 and b = 2. Which of the expressions below equal 6? Select all that do.
Select all that apply.
Hint
Substitute with parentheses, for example b - 2a = 2 - 2(-2). Evaluate every choice; more than one can be correct.
Step-by-step solution
Substitute a = -2 and b = 2 into each expression:
b - 2a = 2 - 2(-2) = 2 + 4 = 6 ✓
2a + b = 2(-2) + 2 = -4 + 2 = -2 ✗
a + 4b = -2 + 4(2) = -2 + 8 = 6 ✓
a - 2b = -2 - 2(2) = -2 - 4 = -6 ✗
ab + 10 = (-2)(2) + 10 = -4 + 10 = 6 ✓
3a = 3(-2) = -6 ✗
The expressions with value 6 are b - 2a, a + 4b and ab + 10.
Check: the three wrong choices give -2, -6 and -6. Two of them give -6, the opposite of 6 - a sign slip would make them look right, so watch the signs.
Tip:ab means a \times b. With one negative and one positive factor, the product is negative.
Question 20 of 36
Fill in
When x = 3, the expression kx + 7 equals -5. Find the number k.
k =
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Substitute x = 3 to get an equation with k in it. Then undo the +7 and the multiplication by 3.
Step-by-step solution
Substitute x = 3: k(3) + 7 = -5, that is 3k + 7 = -5.
Subtract 7 from both sides: 3k = -5 - 7 = -12.
Divide both sides by 3: k = -12 \div 3 = -4.
The value is k = -4.
Check: the expression is -4x + 7. At x = 3: -4(3) + 7 = -12 + 7 = -5 ✓
Tip: "the expression has a value of -5 when x = 3" is a hidden equation. Substitute, set it equal to the value, and solve.
Question 21 of 36
Jordan evaluated 10 - 4x when x = -2:
Step 1: 10 - 4(-2)
Step 2: 6(-2)
Step 3: -12
Which statement is true?
Hint
Look at Step 2. What should be done first in 10 - 4(-2): the subtraction or the multiplication?
Step-by-step solution
Step 1 is correct: the value -2 is substituted in parentheses.
Step 2 is wrong: Jordan did 10 - 4 = 6 first. Multiplication must come before subtraction.
The true statement is Step 2 is wrong; he should multiply first, and the correct value is 18.
Check: read -4x as (-4)(x): (-4)(-2) = +8, and 10 + 8 = 18 ✓
Tip: the number right in front of a variable is glued to it by multiplication. Never "borrow" it to subtract from the number before it.
Question 22 of 36
A parking garage charges $4 to enter plus $2.75 per hour. The cost, in dollars, for h hours is 4 + 2.75h.
Lena paid $26 for parking. For how many hours did she park?
Hint
Set the expression equal to 26. Take away the entry fee first, then divide by the hourly rate.
Step-by-step solution
Write the equation: 4 + 2.75h = 26.
Subtract the entry fee: 2.75h = 26 - 4 = 22.
Divide by the hourly rate: h = 22 \div 2.75 = 8.
Lena parked for 8 hours.
Check:4 + 2.75(8) = 4 + 22 = 26 ✓
Tip: in "work backwards" money problems, the fixed fee comes off first because it was added last. Undo operations in the reverse order: first undo the addition (subtract 4), then undo the multiplication (divide by 2.75). You can also test the answer choices by plugging each one into 4 + 2.75h.
Question 23 of 36
Fill in
The expression 3x - k has a value of 20 when x = -4.
What is the value of k?
k =
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Substitute x = -4, set the expression equal to 20, and solve for k. Watch the signs.
Step-by-step solution
Substitute x = -4: 3(-4) - k = 20.
Multiply: -12 - k = 20.
Add 12 to both sides: -k = 32.
Multiply both sides by -1: k = -32.
The value is k = -32.
Check:3(-4) - (-32) = -12 + 32 = 20 ✓
Tip: if you get k = 32, the check shows -12 - 32 = -44, not 20. Always substitute your answer back in. A missing constant can be negative. Also note that -k = 32 is not the final answer: you still have to multiply (or divide) both sides by -1.
Question 24 of 36
What is the value of the expression below when a = -2, b = 5 and c = -3?
\frac{2a - b}{c} - 3(a + c)
Hint
Work out the numerator 2a - b, divide by c, then find a + c. Track every sign.
Step-by-step solution
Numerator: 2a - b = 2(-2) - 5 = -4 - 5 = -9.
Divide by c: \dfrac{-9}{-3} = 3 (negative ÷ negative is positive).
Parentheses: a + c = -2 + (-3) = -5.
Multiply: -3(-5) = 15.
Combine: 3 - 3(a + c) = 3 + 15 = 18.
The value is 18.
Check: on the calculator: (2×((−)2)−5)÷((−)3)−3×((−)2+(−)3)enter → 18 ✓
Tip: in a long expression, find each piece separately and write it down, then put the pieces together. This keeps each sign decision small.
Question 25 of 36
Fill in
Two gyms charge these amounts, in dollars, for m months of membership:
Gym A: 30 + 12m
Gym B: 90 + 7m
For a 9-month membership, how many dollars less does the cheaper gym cost?
dollars
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Evaluate both expressions at m = 9. The question asks for the difference, not either total.
Step-by-step solution
Gym A: 30 + 12(9) = 30 + 108 = 138 dollars.
Gym B: 90 + 7(9) = 90 + 63 = 153 dollars.
Gym A is cheaper. The difference is 153 - 138 = 15.
The cheaper gym costs 15 dollars less.
Check: Gym B costs $60 more up front but $5 less per month. After 9 months it has saved 9 \times 5 = 45 dollars, so it is still 60 - 45 = 15 dollars more expensive ✓
Tip: read the last line of the question again before you answer. Here, 138 and 153 are steps, and the answer is their difference.
Question 26 of 36
Drag and drop
Drag a value into each empty box to complete the table for the expression -2x + 5. Not every tile is used.
x
-3
0.5
4
-2x + 5
Tap a tile, then tap a box to place it.
Hint
The coefficient is -2. For x = -3, think: negative times negative.
Step-by-step solution
x = -3: -2(-3) + 5 = 6 + 5 =11.
x = 0.5: -2(0.5) + 5 = -1 + 5 =4.
x = 4: -2(4) + 5 = -8 + 5 =-3.
Unused tiles: -1 comes from (-2)(-3) = -6 (sign error), and 13 comes from (-2)(4) = +8 (sign error).
Check: as x goes up, -2x + 5 should go down (the coefficient is negative). The values 11, 4, -3 go down ✓. The step from x = 0.5 to x = 4 is 3.5, and 3.5 \times (-2) = -7: 4 - 7 = -3 ✓
Tip: a negative coefficient makes the values decrease as x increases. If your table goes up, look for a sign error.
Question 27 of 36
What is the value of 4r - 2s + t when r = -1.5, s = -3 and t = -8?
Hint
Substitute all three values in parentheses: 4(-1.5) - 2(-3) + (-8). Do each product, then add and subtract left to right.
Step-by-step solution
Substitute: 4(-1.5) - 2(-3) + (-8).
4(-1.5) = -6.
-2(-3) = +6.
Adding -8 is the same as subtracting 8.
Combine: -6 + 6 - 8 = -8.
The value is -8.
Check: the first two parts cancel (-6 + 6 = 0), so the answer is just t = -8 ✓
Tip: with three or more variables, write the substituted line in full before calculating. Most errors happen when values are plugged in "in your head".
Question 28 of 36
Drop-down
Kim evaluated \dfrac{x + 9}{3} when x = 6. Her work was:
6 + 9 \div 3 = 6 + 3 = 9
Select the answers that make the statements true.
Kim's mistake was .
The correct value is .
Choose an answer from each menu.
Hint
What does the fraction bar do to the whole top, x + 9?
Step-by-step solution
The fraction bar means "divide the whole top by the bottom". It acts like parentheses: \dfrac{x + 9}{3} = (x + 9) \div 3.
Kim divided only the 9 by 3, so her mistake was dividing only 9 by 3.
Correct work: top 6 + 9 = 15, then 15 \div 3 = 5.
The correct value is 5.
Check:5 \times 3 = 15, and 15 = 6 + 9 ✓
Tip: when you rewrite a fraction on one line (or type it into the calculator), put parentheses around the top and around the bottom.
Question 29 of 36
Fill in
Water boils at a lower temperature at high elevations. One estimate for the boiling point, in °F, at an elevation of h feet is
212 - 0.0018h
Use the expression to estimate the boiling point of water in Denver, at an elevation of 5,280 feet. Round your answer to the nearest tenth of a degree.
°F
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Multiply 0.0018 \times 5{,}280 first. Round only at the very end.
Step-by-step solution
Substitute: 212 - 0.0018(5{,}280).
Multiply: 0.0018 \times 5{,}280 = 9.504.
Subtract: 212 - 9.504 = 202.496.
Round to the nearest tenth: the hundredths digit is 9, so round up: 202.5.
The boiling point in Denver is about 202.5°F.
Check: estimate: 0.002 \times 5{,}000 = 10, so the boiling point is about 212 - 10 = 202 ✓ - close to 202.5.
Tip: do not round in the middle of a problem. Rounding 9.504 to 10 first would give 202, which is not correct to the nearest tenth.
Question 30 of 36
Select all
Let x = -\tfrac{1}{2}. Mark every expression below whose value is 4.
Select all that apply.
Hint
It may help to use the decimal x = -0.5. Substitute in parentheses and watch every sign.
Step-by-step solution
Substitute x = -\tfrac{1}{2} = -0.5:
6 - 4x = 6 - 4(-0.5) = 6 + 2 = 8 ✗
3 - 2x = 3 - 2(-0.5) = 3 + 1 = 4 ✓
-8x = -8(-0.5) = 4 ✓
2x + 3 = 2(-0.5) + 3 = -1 + 3 = 2 ✗
12x + 10 = 12(-0.5) + 10 = -6 + 10 = 4 ✓
8x = 8(-0.5) = -4 ✗
The expressions with value 4 are 3 - 2x, -8x and 12x + 10.
Check: with the fraction: -8 \cdot \left(-\tfrac{1}{2}\right) = \tfrac{8}{2} = 4 ✓ and 12 \cdot \left(-\tfrac{1}{2}\right) = -6, so -6 + 10 = 4 ✓
Tip: multiplying by -\tfrac{1}{2} is the same as halving and changing the sign. That makes these quick to do without a calculator.
Question 31 of 36
A taxi company uses this rule for fares, in dollars:
3.50 + 2.25m + 0.40w
where m is the number of miles and w is the number of minutes spent waiting in traffic. Rosa's fare for a 9.6-mile ride was $27.50.
How many minutes did her taxi spend waiting?
Hint
Substitute m = 9.6 and set the expression equal to 27.50. Subtract everything you know, then divide.
Tip: you can also plug in the answer choices. Only w = 6 makes the fare exactly $27.50. Plugging in is a great backup when you are unsure of the algebra.
Question 32 of 36
The expression ax + b has a value of 11 when x = 2, and a value of -4 when x = -3.
What is the value of the expression when x = 6?
Hint
Write two equations: 2a + b = 11 and -3a + b = -4. Subtracting one from the other removes b.
Step-by-step solution
From the facts: 2a + b = 11 and -3a + b = -4.
Subtract the second equation from the first: (2a + b) - (-3a + b) = 11 - (-4), so 5a = 15 and a = 3.
Find b: 2(3) + b = 11 \Rightarrow b = 5.
The expression is 3x + 5. At x = 6: 3(6) + 5 = 18 + 5 = 23.
The value is 23.
Check:3(2) + 5 = 11 ✓ and 3(-3) + 5 = -4 ✓
Tip: read what the question asks for at the end. Finding a and b is only the middle of this problem.
Question 33 of 36
Fill in
An electrician charges a $75 call fee plus $58 per hour of work, and adds the cost of parts. The bill, in dollars, is
75 + 58h + p
where h is the number of hours and p is the cost of parts. One bill was $480.50, and the parts cost $57.50.
How many hours did the electrician work?
h =
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Substitute the bill and the parts cost. Then remove everything that is not hours before you divide.
Step-by-step solution
Substitute: 75 + 58h + 57.50 = 480.50.
Combine the known amounts: 75 + 57.50 = 132.50, so 58h + 132.50 = 480.50.
Tip: the totals here are close ($19.40 vs $19.70). When choices are close, estimating is not enough - compute each total carefully.
Question 35 of 36
A student made a table of values for the expression \dfrac{3x - 4}{2}.
x
-2
0
1.5
6
\dfrac{3x - 4}{2}
-1
-2
0.25
7
Which column contains an error?
Hint
Recompute each value: the whole top first, then divide by 2.
Step-by-step solution
x = -2: top 3(-2) - 4 = -6 - 4 = -10, and -10 \div 2 = -5. The table says -1. Error.
x = 0: top 0 - 4 = -4, and -4 \div 2 = -2 ✓
x = 1.5: top 4.5 - 4 = 0.5, and 0.5 \div 2 = 0.25 ✓
x = 6: top 18 - 4 = 14, and 14 \div 2 = 7 ✓
The error is in the x = -2 column. The student probably computed -6 + 4 = -2 on top.
Check: the expression equals 1.5x - 2, so values rise by 1.5 for each 1 in x. From x = -2 to x = 0 (2 steps) the value must rise by 3: -5 + 3 = -2 ✓. From -1 it would reach 2, not -2.
Tip: a table of a linear expression has a steady pattern. A value that breaks the pattern is the first place to look for an error.
Question 36 of 36
Leo evaluated \dfrac{a - 3b}{a + b} when a = 2 and b = -4:
Step 1: \dfrac{2 - 12}{2 - 4}
Step 2: \dfrac{-10}{-2}
Step 3: 5
Which statement is true?
Hint
Check Step 1 carefully. What is -3 \times (-4)?
Step-by-step solution
Top: a - 3b = 2 - 3(-4). Since 3(-4) = -12, this is 2 - (-12) = 2 + 12 = 14.
Leo wrote 2 - 12, so his numerator in Step 1 is wrong.
Bottom: a + b = 2 + (-4) = -2. Leo's denominator is right.
Correct value: \dfrac{14}{-2} = -7.
The true statement is Step 1 is wrong: the numerator should be 2 + 12, and the value is -7.
Check:-7 \times (-2) = 14 ✓, and 14 is the correct numerator.
Tip: "minus a negative" is the most common GED trap in evaluation. Write -3(-4) with parentheses, and you will see the +12.
