The equation 34(8x - 12) = 2(x + k), where k is a constant... | SAT Linear equations in one variable Question, Answer Explained

Question bank / Linear equations in one variable

Math · AlgebraMedium

The equation $\frac{3}{4}(8x - 12) = 2(x + k)$ , where $k$ is a constant, has the solution $x = 5$ . What is the value of $k$ ?

Student-produced response: enter your answer.

Show answer and explanation

Answer: 11/2

Substitute $x = 5$ . The left side is $\frac{3}{4}(40 - 12) = \frac{3}{4}(28) = 21$ . The right side is $2(5 + k) = 10 + 2k$ . So $10 + 2k = 21$ , which gives $2k = 11$ and $k = 5.5$ .

Forgetting to multiply $k$ by $2$ gives $10 + k = 21$ and $k = 11$ .

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free, or take a free full-length practice test.