SAT Linear equations in one variable Practice Question 15 (Hard)

Question bank / Linear equations in one variable

Math · AlgebraHard

In the equation $kx - 5 = 3(2x + 1) - 10$ , $k$ is a constant. If the equation has no solution, what is the value of $k$ ?

$-6$

$2$

$3$

$6$

Show answer and explanation

Answer: D

Simplify the right side: $6x + 3 - 10 = 6x - 7$ . The equation is $kx - 5 = 6x - 7$ . A linear equation has no solution when the $x$ -coefficients are equal and the constants differ. If $k = 6$ , the equation becomes $-5 = -7$ , which is never true, so $k = 6$ .

Choice C uses the coefficient 3 from before distributing, but the right side has an $x$ -coefficient of 6.

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