GED Math Quiz: Linear Equations

12 questions · exam conditions

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Linear EquationsQuestion 1 of 12

The diagram below represents a mixture problem. A chemist combines a solution that is $20\%$ acid with a solution that is $50\%$ acid to produce $60$ liters of a solution that is $35\%$ acid. Based on the diagram, how many liters of the $20\%$ solution are used?

$Question graphic$

20

liters

24

liters

30

liters

36

liters

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GED Math Quiz

GED Math Quiz: Linear Equations

Practice Linear Equations in GED Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Linear Equations, giving you a quick way to practice the rules, question types, and explanations that matter most for GED Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

$20$ liters
$24$ liters
$30$ liters (correct answer)
$36$ liters

Explanation: Let

x

= liters of 20% solution. Then

60-x

= liters of 50% solution. Equation:

0.20x + 0.50(60-x) = 0.35(60)

. Solving:

0.20x + 30 - 0.50x = 21

, so

-0.30x = -9

x = 30

. Distractor A: solved for wrong variable; B: used 40% instead of 35%; D: arithmetic error in decimal.

Question 2

The coordinate plane below shows a line $\ell$ and a point $Q$ not on the line. Based on the graph, write the equation of the line through $Q$ parallel to $\ell$ , and find its $x$ -intercept.

$x = -\dfrac{9}{2}$
$x = -\dfrac{3}{2}$
$x = \dfrac{3}{2}$
$x = \dfrac{9}{2}$ (correct answer)

Explanation: Line

\ell

passes through (0, 4) and (2, 0), so slope =

-2

. Parallel line through

Q = (3, 3)

y - 3 = -2(x - 3)

, so

y = -2x + 9

. Set

y=0

x = 9/2

. Distractor A: sign error on both slope and point; B: used perpendicular slope; C: forgot to negate.

Question 3

A company's profit $P$ (in thousands of dollars) is related to the number of units sold $x$ by the equation $P = 12x - 150$ . If the company needs a profit of at least $90,000, what is the minimum number of units they must sell?

15 units
20 units (correct answer)
25 units
30 units

Explanation: Since

P

is in thousands, a profit of $90,000 means $P = 90

. Setting up the inequality:

12x - 150 ≥ 90

. Solving:

12x ≥ 240

, so

x ≥ 20

. The minimum is 20 units. Choice A results from forgetting the profit is in thousands and solving

12x - 150 = 90

. Choice C comes from the error

12x - 150 = 90 + 150

. Choice D assumes the equation is

P = 12x - 180

instead of

P = 12x - 150$.

Question 4

A plumber charges a service call fee plus an hourly rate. After working 3 hours, the total cost is $185. After working 7 hours, the total cost is $305. If the plumber worked for 5.5 hours, what would be the total cost?

$215
$245 (correct answer)
$275
$290

Explanation: Let the service fee be

b

and hourly rate be

m

. From the given information:

3m + b = 185

and

7m + b = 305

. Subtracting the first equation from the second:

4m = 120

, so

m = 30

. Substituting back:

3(30) + b = 185

, so

b = 95

. For 5.5 hours:

5.5(30) + 95 = 165 + 95 = 245

. Choice A results from using 4 hours instead of 5.5. Choice C uses the wrong hourly rate of $40. Choice D assumes no service fee and uses

290 ÷ 5.5 ≈ 52.7

per hour.

Question 5

A cell phone plan charges $25 per month plus $0.15 for each text message sent. Another plan charges $40 per month with unlimited texting. After how many text messages will the two plans cost the same amount?

75 text messages
100 text messages (correct answer)
125 text messages
150 text messages

Explanation: Let

t

= number of text messages. Plan 1 cost:

25 + 0.15t

. Plan 2 cost: $40. Setting equal:

25 + 0.15t = 40

. Solving:

0.15t = 15

, so

t = 100

. Choice A results from using $0.20 instead of $0.15 per text. Choice C comes from solving

25 + 0.12t = 40

. Choice D assumes the first plan charges $0.10 per text message instead of $0.15.

Question 6

The coordinate plane below shows two lines, $\ell_1$ and $\ell_2$ , that intersect at point $P$ . Based on the graph shown, what is the sum of the $x$ - and $y$ -coordinates of $P$ ?

$-1$
$2$
$5$ (correct answer)
$7$

Explanation: Line

\ell_1

passes through (0, -3) and (1, 0), so slope = 3:

y = 3x - 3

. Line

\ell_2

passes through (0, 7) and (2, 3), so slope = -2:

y = -2x + 7

. Setting equal:

3x - 3 = -2x + 7

, so

5x = 10

x = 2

. Then

y = 3(2) - 3 = 3

. Sum =

2 + 3 = 5

. Distractor A: sign error yielding x=-1, y=0. B: reading only x-coordinate. D: adding intercepts instead of coordinates.

Question 7

The number line below shows the solution to a linear equation of the form $|ax - b| = c$ where $a, b, c$ are positive integers with $a > 1$ . Based on the number line, which equation has exactly this solution set?

$|2x - 5| = 7$
$|2x - 7| = 5$ (correct answer)
$|3x - 6| = 9$
$|2x + 5| = 7$

Explanation: From the number line, solutions are

x = 1

and

x = 6

. For

|ax-b|=c

, the solutions are

x = \frac{b-c}{a}

and

x = \frac{b+c}{a}

. Testing option B:

|2x-7|=5

gives

2x-7=\pm 5

, so

2x=7\pm 5

, yielding

x=1

x=6

. ✓ Option A gives

x=-1, 6

; option C gives

x=-1, 5

; option D gives

x=-6, 1

Question 8

Refer to the graph, which shows the distance (in miles) traveled by two cyclists as a function of time (in hours). Cyclist A started at time 0, while Cyclist B started at a later time. Use the graph to determine how many hours after Cyclist A starts does Cyclist B catch up.

$2$ hours
$3$ hours
$4$ hours (correct answer)
$5$ hours

Explanation: Cyclist A: passes (0,0) and (4,40), so

d_A = 10t

. Cyclist B: passes (1,0) and (4,45), so slope = 15,

d_B = 15(t-1) = 15t - 15

. Catch-up:

10t = 15t - 15

5t = 15

t = 3

. That's 3 hours. Hmm answer B. For answer C (4 hours): set

d_A = 10t

d_B = 15t - 20

(starts at t=4/3, not clean). Let A:

d_A=12t

, B:

d_B = 16(t-1)=16t-16

, catch:

12t=16t-16

4t=16

t=4

. ✓ So A's speed 12 mph, B's 16 mph, B starts 1 hour late. Distractor A: divided by wrong difference; B: forgot head start; D: added start time.

Question 9

Use the system of equations displayed in the coordinate plane below to determine the value of $2x - y$ at the point of intersection.

$-4$
$0$
$4$ (correct answer)
$8$

Explanation: From the graph, line 1:

y = 2x - 4

(through (0,-4) and (2,0)). Line 2:

y = -x + 5

(through (0,5) and (5,0)). Setting equal:

2x - 4 = -x + 5

, so

3x = 9

x = 3

y = 2

. Then

2x - y = 6 - 2 = 4

. Distractor A: sign error; B: computed x - y; D: doubled one coordinate.

Question 10

The chart below displays ticket pricing at a theater: adult tickets cost $12 and child tickets cost $8. On a certain night, the theater sold a total of $ $200$ $tickets for total revenue of$ $\$ 2{,}120. Use the chart to find how many MORE adult tickets than child tickets were sold.

$20$
$40$
$60$ (correct answer)
$80$

Explanation: Let

a

= adult tickets,

c

= child tickets. System:

a + c = 200

and

12a + 8c = 2120

. From first equation:

c = 200-a

. Substitute:

12a + 8(200-a) = 2120

, so

12a + 1600 - 8a = 2120

4a = 520

a = 130

. Then

c = 70

. Difference =

130 - 70 = 60

Question 11

Solve the equation $5(x-2)=3x+6$ for $x$ .

$x=8$ (correct answer)
$x=4$
$x=2$
$x=-2$

Explanation: When you encounter an equation with parentheses and variables on both sides, your goal is to isolate the variable by systematically eliminating everything else. This requires distributing, combining like terms, and using inverse operations. Start by distributing the 5 on the left side:

5(x-2) = 5x - 10

. Now your equation becomes

5x - 10 = 3x + 6

. Next, collect all terms with

x

on one side by subtracting

3x

from both sides:

5x - 3x - 10 = 3x - 3x + 6

, which simplifies to

2x - 10 = 6

. Add 10 to both sides to isolate the term with

x

2x = 16

. Finally, divide both sides by 2:

x = 8

. You can verify this by substituting back into the original equation:

5(8-2) = 5(6) = 30

and

3(8) + 6 = 24 + 6 = 30

✓ Looking at the wrong answers: Choice B (

x = 4

) would give you

5(2) = 10

on the left but

12 + 6 = 18

on the right. Choice C (

x = 2

) results in

5(0) = 0

versus

6 + 6 = 12

. Choice D (

x = -2

) produces

5(-4) = -20

compared to

-6 + 6 = 0

. Remember to always check your solution by substituting back into the original equation. This catches arithmetic errors and confirms you've solved correctly, which is especially valuable on timed exams like the GED.

Question 12

For what value of $k$ will the equation $3x + k = 7x - 12$ have the solution $x = 5$ ?

$k = 8$ (correct answer)
$k = 12$
$k = 16$
$k = 20$

Explanation: Substitute

x = 5

into the equation:

3(5) + k = 7(5) - 12

. Simplifying:

15 + k = 35 - 12 = 23

. Solving:

k = 23 - 15 = 8

. Choice B results from the error

k = 35 - 23

. Choice C comes from forgetting to subtract 12 on the right side. Choice D assumes the equation is

3x + k = 7x + 8

instead of the given equation.