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Linear equations in one variable — SAT practice questions

Linear equations in one variable on the SAT Math section cover solving equations that reduce to a single unknown of degree one, including word problems and equations with a parameter. A student must isolate the unknown, tell when there is no solution or infinitely many solutions, and sometimes find a related expression rather than the variable itself. Questions often take the form of a mixture story, a short equation that asks for a transformed quantity, or a constant that makes the equation an identity. Traps include distributing incorrectly, answering the wrong target, and mixing up unique and infinitely many solutions. Choices are usually numbers.

  • Section: Math 44 questions on the paper
  • 134 practice questions in the app

Sample questions

Question 1

A 40-liter mixture is 20%20\% acid. How many liters of a 50%50\% acid solution must be added to make the resulting mixture 30%30\% acid?

  1. A10
  2. B16
  3. C20
  4. D24
Show answer

Answer: C — 20

If xx liters are added, then 0.20(40)+0.50x=0.30(40+x)0.20(40)+0.50x=0.30(40+x). This gives 8+0.5x=12+0.3x8+0.5x=12+0.3x, so x=20x=20.

Question 2

If 12x−27=4512x-27=45, what is the value of 4x−94x-9?

  1. A9
  2. B15
  3. C18
  4. D45
Show answer

Answer: B — 15

Notice that 4x−9=13(12x−27)4x-9=\dfrac{1}{3}(12x-27). Since 12x−27=4512x-27=45, we get 4x−9=453=154x-9=\dfrac{45}{3}=15.

Question 3

r(5x−2)+8x=38x−12r(5x-2)+8x=38x-12

In the given equation, rr is a constant. The equation has infinitely many solutions. What is the value of rr?

  1. A-6
  2. B6
  3. C465\dfrac{46}{5}
  4. D12
Show answer

Answer: B — 6

Expanding the left side gives (5r+8)x−2r(5r+8)x-2r. Matching both sides requires 5r+8=385r+8=38 and −2r=−12-2r=-12, and both conditions give r=6r=6.

Practice 134 Linear equations in one variable questions in the app

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