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Linear equations and expressions in one variable — ACT practice questions

Linear equations and expressions in one variable on the ACT Mathematics test cover writing, rearranging, and evaluating linear relationships with a single unknown. A student must translate a cost or rate situation into an equation, isolate a requested letter in a multi-letter identity, and substitute a given value into a nested linear expression. Questions usually appear as short word problems or algebraic prompts asking for a specific variable or a numerical value. Answer choices tend to be simplified expressions or integers, with traps such as mixing a one-time fee with a repeating charge, dropping a negative when distributing, and combining unlike terms.

  • Section: Mathematics 45 questions on the paper
  • 55 practice questions in the app

Sample questions

Question 1

A gym membership costs a one-time enrollment fee of 45 dollars plus 30 dollars per month. Malia has spent a total of 255 dollars on her membership so far. How many months has she been a member?

  1. A5
  2. B7
  3. C8
  4. D10
Show answer

Answer: B — 7

Let m be the number of months: 45 + 30m = 255. Subtract 45: 30m = 210. Divide by 30: m = 7.

Question 2

If 2a−3b=5c+72a - 3b = 5c + 7, then b=?b = ?

  1. A2a−5c−73\dfrac{2a - 5c - 7}{3}
  2. B2a−5c−72a - 5c - 7
  3. C2a−5c+73\dfrac{2a - 5c + 7}{3}
  4. D5c+7−2a3\dfrac{5c + 7 - 2a}{3}
Show answer

Answer: A — 2a−5c−73\dfrac{2a - 5c - 7}{3}

Subtract 2a from both sides: -3b = 5c + 7 - 2a. Divide by -3, flipping every sign: b = (2a - 5c - 7)/3.

Question 3

For x=−3x = -3, what is the value of 4(2x−1)−3(x+2)+54(2x - 1) - 3(x + 2) + 5?

  1. A-20
  2. B-17
  3. C-8
  4. D10
Show answer

Answer: A — -20

Distributing and combining like terms gives 8x−4−3x−6+5=5x−58x - 4 - 3x - 6 + 5 = 5x - 5. Substituting x=−3x = -3 gives 5(−3)−5=−205(-3) - 5 = -20.

Practice 55 Linear equations and expressions in one variable questions in the app

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