Linear equations and expressions in one variable — ACT practice questions

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Practice 61 Linear equations and expressions in one variable questions in the app

What this topic is

Linear equations and expressions in one variable involve a variable raised only to the first power, and most have exactly one solution, found by undoing operations in reverse order.

When the variable cancels, the equation has no solution if a false statement remains and infinitely many if a true one remains. A typical word problem pairs a starting fee with a charge per unit and asks how many units match a total: subtract the fee, then divide by the per-unit charge.

Other items solve a formula for one letter or substitute a negative number. Many wrong choices come from mishandling a minus sign across parentheses.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Easier

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?

5✗ Not this one7✓ Correct8✗ Not this one10✗ Not this one

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Answer: B — 7

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

Question 2Easier

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

\frac{2 a - 5 c - 7}{3}

✓ Correct

2 a - 5 c - 7

✗ Not this one

\frac{2 a - 5 c + 7}{3}

✗ Not this one

\frac{5 c + 7 - 2 a}{3}

✗ Not this one

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Answer: A — $\frac{2 a - 5 c - 7}{3}$

Subtract $2 a$ from both sides: $- 3 b = 5 c + 7 - 2 a$ . Divide by $- 3$ , flipping every sign: $b = \frac{2 a - 5 c - 7}{3}$ .

Question 3Easier

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

- 20

✓ Correct

- 17

✗ Not this one

- 8

✗ Not this one10✗ Not this one

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Answer: A — $- 20$

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

Every question is picked for where you are right now, wrong answers come back until they stick, and it all works offline.

Practice 61 Linear equations and expressions in one variable questions in the app

Linear equations and expressions in one variable — ACT practice questions

What this topic is

Sample questions

More ACT topics

Mathematics