ACT · Math · Preparing for Higher Math: Algebra

Linear equations

Linear equations is part of Preparing for Higher Math: Algebra in the ACT Math section. The questions below are written in the style of the real test, each with the answer and a worked explanation.

Question types you will see here include multi-step linear equation, equation from a fixed-fee-plus-rate context, solve a formula for one variable and find an expression's value without solving.

Common traps: sign error when distributing a negative; combining unlike terms; dividing only one term by the coefficient.

Sample questions

Question 1
If 3x + 13 = 4x + 17, what is the value of x?
- A.
  -30
- B.
  -4
- C.
  4/7
- D.
  4
Answer: B. -4
Subtract 4x from both sides to get -x + 13 = 17. Subtract 13 from both sides: -1x = 4. Divide by -1: x = -4.
Question 2
If 6x + 6 = 2x - 6, what is the value of x?
- A.
  -3
- B.
  -3/2
- C.
  0
- D.
  3
Answer: A. -3
Subtract 2x from both sides to get 4x + 6 = -6. Subtract 6 from both sides: 4x = -12. Divide by 4: x = -3.
Question 3
A music school charges a $30 registration fee plus $12 per lesson. If Tomás paid a total of $354, how many lessons were paid for?
- A.
  27
- B.
  28
- C.
  29
- D.
  32
Answer: A. 27
Let n be the number of lessons. Then 30 + 12n = 354. Subtract 30: 12n = 324. Divide by 12: n = 27.
Question 4
If 3x + 6 = 2x + 14, what is the value of x?
- A.
  -8
- B.
  8/5
- C.
  8
- D.
  20
Answer: C. 8
Subtract 2x from both sides to get x + 6 = 14. Subtract 6 from both sides: 1x = 8. Divide by 1: x = 8.
Question 5
A car-rental company in Cape Town offers two one-day plans. Plan A costs 350 rand plus 2.50 rand per kilometer driven, and Plan B costs 500 rand plus 1.25 rand per kilometer driven. For how many kilometers driven in one day do the two plans cost the same?
- A.
  120
- B.
  150
- C.
  340
- D.
  375
Answer: A. 120
Set the costs equal: 350 + 2.50k = 500 + 1.25k, so 1.25k = 150 and k = 120 km (both plans then cost 650 rand). Choice B stops at the difference in the daily fees, 150, without dividing by the difference in the per-kilometer rates; choice C divides the sum of the daily fees, 850, by 2.50; choice D multiplies 150 by 2.50 instead of dividing by 1.25.

Find your real gaps

A few questions show the style. The free scan shows which ACT skills cost you the most points, then builds a plan around them.

Take the free scan