SAT Linear equations in one variable Practice Question 19 (Hard)

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Question bank / Linear equations in one variable

Math · AlgebraHard

In the equation $(p - 2)x + 8 = 5x - 2p$ , $p$ is a constant. For what value of $p$ does the equation have no solution?

$-4$

$3$

$5$

$7$

Show answer and explanation

Answer: D

The equation has no solution when the $x$ -coefficients are equal but the constants are not. Set $p - 2 = 5$ , so $p = 7$ . Then the equation is $5x + 8 = 5x - 14$ , and since $8 \ne -14$ , there is no solution.

Choice A makes the constant terms equal ( $8 = 8$ ), but then the $x$ -coefficients differ, so there is exactly one solution.

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