SAT Math
Linear Equations in One Variable
Linear Equations in One Variable is a skill in the Algebra domain of the Digital SAT Math section. These are practice questions on it, and each answer choice comes with an explanation of why it is right or wrong.
11 questions. After every answer you’ll see why each choice is right or wrong, not just the one you picked.
Sample questions
Open a question to see the answer choices and the correct answer.
What value of x satisfies the equation 6x − 15 = 3x + 21?
- A. 4
- B. 12 ✓
- C. 2
- D. 36
Correct answer: B. Subtracting 3x from both sides gives 3x − 15 = 21, and adding 15 to both sides gives 3x = 36, so x = 12.
A caterer's total bill for an event is $1,240. This includes a fixed setup fee of $190 plus a charge per guest that is the same for each of the 150 guests. What is the charge per guest, in dollars?
- A. $8.27
- B. $9.53
- C. $7.00 ✓
- D. $6.56
Correct answer: C. Subtracting the setup fee gives $1,240 − $190 = $1,050, and dividing by 150 guests gives $1,050 ÷ 150 = $7.00 per guest.
How many solutions does the equation 4(2x + 3) − 2x = 6(x + 2) have?
- A. Exactly two solutions
- B. Exactly one solution
- C. No solution
- D. Infinitely many solutions ✓
Correct answer: D. The left side simplifies to 8x + 12 − 2x = 6x + 12, which is identical to the right side, 6x + 12, for every value of x, so every real number is a solution.
What value of x satisfies the equation (2/3)(x − 6) = x/2 + 1?
- A. 30 ✓
- B. 18
- C. 6
- D. −30
Correct answer: A. Correct — multiplying every term by 6 gives 4(x − 6) = 3x + 6, so 4x − 24 = 3x + 6, which gives x = 30.
The perimeter of an isosceles triangle is 61 inches. Each of the two congruent sides is 5 inches longer than the base, b. What is the length, in inches, of one of the congruent sides?
- A. 17
- B. 22 ✓
- C. 20.33
- D. 27
Correct answer: B. Correct — the perimeter equation is 2(b + 5) + b = 61, so 3b + 10 = 61, giving b = 17; each congruent side is then 17 + 5 = 22 inches.