This is an estimate based on your percent correct on our practice tests. The official GED score conversion is not public, so your real score may differ. Scores of 145+ pass; 165+ is College Ready.
Tip: Always put the substituted expression in parentheses, so the 2 multiplies both the 3y and the -1. Writing 2 \cdot 3y - 1 is a very common slip.
Question 2 of 10 · Solve one-variable linear equations
No calculator
Devon solved the equation 4x - 3(x - 2) = 10 as shown.
Step
Work
1
4x - 3x - 6 = 10
2
x - 6 = 10
3
x = 16
In which step did Devon make his first error?
Hint
Check each step separately. What is (-3) \times (-2)?
Step-by-step solution
Check each step.
Step 1: The -3 must multiply both terms in (x - 2): (-3)(x) = -3x and (-3)(-2) = +6. The correct line is 4x - 3x + 6 = 10. Devon wrote -6, so Step 1 is wrong.
Steps 2 and 3 do the right operations on Devon's wrong line, so they only carry the error forward.
Correct solution: 4x - 3x + 6 = 10, so x + 6 = 10, so x = 4.
Tip: Treat "minus a number times parentheses" as multiplying by a negative number. Negative times negative is positive.
Question 3 of 10 · Real-world linear equations
Fill in
A community theater sold 150 tickets for one show. Adult tickets cost $12 and child tickets cost $7. Ticket sales totaled $1,465. How many adult tickets were sold?
adult tickets
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Let a = adult tickets. Then the number of child tickets is 150 - a. Write one equation for the money.
Step-by-step solution
Let a = adult tickets. Then child tickets = 150 - a.
Money from adults: 12a. Money from children: 7(150 - a).
Equation: 12a + 7(150 - a) = 1465.
Distribute: 12a + 1050 - 7a = 1465.
Combine like terms: 5a + 1050 = 1465.
Subtract 1050: 5a = 415. Divide by 5: a = 83.
83 adult tickets were sold (and 150 - 83 = 67 child tickets).
Tip: When two quantities share a known total, name one of them a and write the other as \text{total} - a. This keeps the problem to one variable.
Question 4 of 10 · Write linear equations from context
The perimeter of a rectangle is P = 2l + 2w. Which equation is solved for the width w?
Hint
Treat P and l like numbers. Undo the +\,2l first, then undo the multiplication by 2.
Step-by-step solution
Start with P = 2l + 2w.
Subtract 2l from both sides: P - 2l = 2w.
Divide both whole sides by 2: \dfrac{P - 2l}{2} = w.
The answer is w = \dfrac{P - 2l}{2}.
Check: With numbers, a 5-by-3 rectangle has P = 2(5) + 2(3) = 16. Then w = \dfrac{16 - 2(5)}{2} = \dfrac{6}{2} = 3 ✓
Tip: When you divide, divide the entire side, not just one term. \dfrac{P - 2l}{2} can also be written \dfrac{P}{2} - l.
Question 5 of 10 · Systems of two linear equations
A farm stand sells small baskets of strawberries for $4 and large baskets for $7. One morning it sold 64 baskets and took in $340. How many small baskets were sold?
Hint
Let s = small and \ell = large. Write one equation for the number of baskets and one for the money.
Step-by-step solution
Let s = small baskets, \ell = large baskets.
Baskets: s + \ell = 64
Money: 4s + 7\ell = 340
Multiply the first equation by 4: 4s + 4\ell = 256.
Subtract it from the money equation: (4s + 7\ell) - (4s + 4\ell) = 340 - 256, so 3\ell = 84 and \ell = 28.
Tip: Before you choose an answer, reread which quantity the question asks for. Here the system gives both numbers, and the large-basket count (28) is waiting as a trap.
Question 6 of 10 · Solve one-variable linear equations
Drop-down
Select the choice that makes each statement true.
Equation 1: 2(4x - 1) + 3 = 8x + 1 has .
Equation 2: 5(x + 2) - x = 4x + 1 has .
Choose an answer from each menu.
Hint
Simplify the left side of each equation completely, then compare it with the right side.
Step-by-step solution
Equation 1.
Distribute: 8x - 2 + 3 = 8x + 1.
Combine constants: 8x + 1 = 8x + 1.
Both sides are identical. Subtracting 8x gives 1 = 1, which is always true → infinitely many solutions.
Equation 2.
Distribute: 5x + 10 - x = 4x + 1.
Combine like terms: 4x + 10 = 4x + 1.
Subtract 4x: 10 = 1, which is never true → no solution.
Answers: Equation 1 has infinitely many solutions; Equation 2 has no solution.
Check: try x = 2 in each. Eq. 1: 2(7) + 3 = 17 and 8(2) + 1 = 17 ✓ (works, like every number). Eq. 2: 5(4) - 2 = 18 and 4(2) + 1 = 9 ✗ (fails, like every number).
Tip: When the x terms cancel, look at what is left: a true statement means every number works; a false statement means no number works.
Question 7 of 10 · Solve one-variable linear equations
Theo solved 0.5(6x + 4) = 2x - 3 as shown.
Step
Work
1
3x + 2 = 2x - 3
2
5x + 2 = -3
3
5x = -5
4
x = -1
Which statement is true?
Hint
Check Step 1 by distributing 0.5 yourself. Then check how Theo moved the 2x term in Step 2.
Step-by-step solution
Check each step.
Step 1:0.5 \cdot 6x = 3x and 0.5 \cdot 4 = 2, so 3x + 2 = 2x - 3 is correct.
Step 2: To remove 2x from the right side, subtract 2x from both sides: 3x - 2x + 2 = -3, which is x + 2 = -3. Theo added2x to the left and got 5x. Step 2 is wrong.
Correct finish: x + 2 = -3, so x = -5.
The true statement is: Step 2 is wrong, and the correct solution is x = -5.
Check:x = -5: left 0.5(6(-5) + 4) = 0.5(-26) = -13; right 2(-5) - 3 = -13 ✓. Theo's answer x = -1: left 0.5(-2) = -1, right -5 ✗.
Tip: A term "moves" across the equals sign by doing the opposite operation on both sides. +2x on the right is removed by subtracting 2x.
Question 8 of 10 · Real-world linear equations
Drag and drop
A tank holds 50 gallons of water. It drains at a steady rate of 2.5 gallons per minute. Drag the correct number of minutes into each box. Two numbers are not used.
The tank holds 20 gallons after minutes.
The tank is empty after minutes.
Tap a tile, then tap a box to place it.
Hint
Water left = 50 - 2.5t. Set this equal to 20, then to 0.
Step-by-step solution
Let t = minutes. The water left in the tank is 50 - 2.5t.
When 20 gallons are left:
50 - 2.5t = 20.
Subtract 50: -2.5t = -30.
Divide by -2.5: t = 12 minutes.
When the tank is empty:
50 - 2.5t = 0.
Add 2.5t: 50 = 2.5t.
Divide by 2.5: t = 20 minutes.
Answer: 12 minutes for 20 gallons; 20 minutes to empty.
Tip: "Holds 20 gallons" means 20 gallons are left, so 30 gallons have drained. Dividing 20 by 2.5 (= 8) finds how long it takes to drain 20 gallons — a different question.
Question 9 of 10 · Real-world linear equations
Fill in
After a 15% raise, Dana now earns $20.70 per hour. What was her hourly pay before the raise?
$ per hour
Type your answer in the box. Fractions like 3/4 are fine.
Hint
Her new pay is her old pay plus 15% of her old pay. Write that as one number times the old pay.
Step-by-step solution
Let w = old hourly pay. The raise is 0.15w, so the new pay is w + 0.15w = 1.15w.
Equation: 1.15w = 20.70.
Divide by 1.15: w = \dfrac{20.70}{1.15} = 18.
Her pay before the raise was $18.00 per hour.
Check: 15% of $18 is 0.15 \times 18 = \$2.70, and 18 + 2.70 = \$20.70 ✓
Tip: Do not take 15% off the new amount: 20.70 - 0.15(20.70) \approx 17.60 is wrong, because the raise was 15% of the old pay. Divide by 1.15 instead.
Question 10 of 10 · Write linear equations from context
After an oven is turned off, its temperature drops at a steady rate. The table shows the temperature T, in °F, m minutes after it was turned off.
Minutes, m
3
7
10
15
Temperature, T (°F)
314
266
230
170
Which equation models the oven temperature?
Hint
The minutes are not evenly spaced. Divide each change in temperature by the matching change in minutes. Then work back to m = 0.
Step-by-step solution
Rate: from 3 to 7 minutes, T drops 314 - 266 = 48° in 7 - 3 = 4 minutes: \tfrac{-48}{4} = -12° per minute. Confirm with another pair: from 10 to 15 minutes, \tfrac{170 - 230}{5} = \tfrac{-60}{5} = -12 ✓
Starting value: go back 3 minutes from m = 3: 314 + 3 \times 12 = 314 + 36 = 350°F.
Tip: With uneven steps in a table, never use a single jump in y as the rate — always divide by the jump in x. And the first row shown is not always x = 0.