Skip to content

Math: Algebra, 3 original questions

SAT One-Variable Linear Equations Practice: Questions and Answers

Solve and interpret one-variable linear equations with three original SAT-style questions. Practice distribution, contextual setup and equations with many solutions.

On this page

The short answer

A one-variable linear equation balances two expressions involving the same unknown. Distribute carefully, combine like terms and apply the same operation to both sides until the variable is isolated. In a word problem, define the unknown and write the fixed and changing quantities separately. Not every equation has exactly one solution: canceling variables may leave a true statement or a contradiction. Check a proposed value in the original equation and interpret its units before answering.

Method at a glance

  1. 1Define the unknown
  2. 2Simplify both sides
  3. 3Preserve the balance
  4. 4Check the remaining statement

Try the 3 questionsRead the full method

Step-by-step method

Use these steps in order, then apply them to the questions below.

  1. Step 1: Define the unknown

    For context questions, state what the variable counts or measures. Separate any fixed amount from the per-unit amount.

  2. Step 2: Simplify both sides

    Distribute through every term inside parentheses and combine like terms before moving variable terms.

  3. Step 3: Preserve the balance

    Add, subtract, multiply or divide both sides by the same permitted quantity. Never divide by zero.

  4. Step 4: Check the remaining statement

    An isolated variable gives a candidate. A true constant statement gives all real inputs; a contradiction gives no solution.

Try 3 SAT-style questions

These are original SAT-style questions written by PeakSAT, not official College Board questions. Choose an answer and check it to see why each choice is right or wrong, or open the worked answer.

No sign-in needed. Your answers stay on this page and are not stored.

Question 1 of 3

What value of x satisfies 4(2x − 3) = 3x + 18?

Choose an answer for question 1
View worked answer for question 1

Correct answer

Choice B: 6

Explanation

Distribute to get 8x − 12 = 3x + 18. Subtract 3x and add 12: 5x = 30, so x = 6. Checking gives 4(12 − 3) = 36 and 18 + 18 = 36.

Why each choice is right or wrong

  1. Choice A

    This divides 30 by 8 before removing the 3x term.

  2. Choice B

    Correct answer

    Correct: distributing and balancing gives x = 6.

  3. Choice C

    At x = 10, the two sides are 68 and 48, so they are unequal.

  4. Choice D

    30 is the value of 5x, not x.

Question 2 of 3

An equipment rental costs a fixed $14 fee plus $6 per hour. The total charge is $62. How many hours were charged?

Choose an answer for question 2
View worked answer for question 2

Correct answer

Choice A: 8

Explanation

Let h be the charged hours. The equation is 14 + 6h = 62. Subtract the fixed fee to get 6h = 48, then divide by 6 to obtain h = 8. The check is 14 + 6 × 8 = 62.

Why each choice is right or wrong

  1. Choice A

    Correct answer

    Correct: the variable portion is $48, which pays for 8 hours.

  2. Choice B

    Ten hours would cost $74, exceeding the stated total.

  3. Choice C

    Twelve hours would cost $86, not $62.

  4. Choice D

    48 is the variable charge in dollars, not the number of hours.

Question 3 of 3

Which choice describes all real solutions of 5(x + 2) = 5x + 10?

Choose an answer for question 3
View worked answer for question 3

Correct answer

Choice D: Every real x is a solution

Explanation

Distributing on the left gives 5x + 10 = 5x + 10. Subtracting 5x leaves 10 = 10, a true statement regardless of x. The equation is an identity, so every real x is a solution.

Why each choice is right or wrong

  1. Choice A

    Zero works, but it is not the only value that works.

  2. Choice B

    Two works, but all other real values work as well.

  3. Choice C

    The simplified equation is true, not a contradiction.

  4. Choice D

    Correct answer

    Correct: both sides are the same expression for every real input.

Common mistakes

  • Distributing a multiplier to only one term inside parentheses. Multiply every term before combining.

  • Using a total charge as the per-unit rate. Separate a starting fee from the amount that depends on the unknown.

  • Assuming canceled variables mean x = 0. Decide whether the remaining statement is always true or impossible.

Keep practicing

Everything on this page is free to use. Practicing this skill in the PeakSAT app requires a subscription; one SAT-style assessment is free.

Subscription

One-Variable Linear Equations practice in PeakSAT

Sign in to keep practicing this skill with more SAT-style questions and explanations in the PeakSAT app.

Full access requires a subscription.

Continue One-Variable Linear Equations practiceSee pricing

Free

Take one free SAT-style assessment

See your estimated score and missed questions by skill. Google sign-in, no card required.

Take a free assessment

Common questions

What does 0 = 0 mean after simplifying?

It means the equation is true for every permitted input. In an unrestricted linear equation, that gives all real numbers.

What does 0 = 7 mean?

It is a contradiction, so no value of the variable satisfies the equation.

How can I check a word-problem equation?

Substitute the proposed value, attach its units and verify that the fixed and variable quantities reproduce the stated total.

Sources

  1. College Board: Algebrasatsuite.collegeboard.org
  2. College Board: Student Question Bank Math skillssatsuite.collegeboard.org

Sources are linked for reference; they do not endorse PeakSAT. How we prepare our guides