Which of the following represents all solutions to the... | SAT Linear inequalities in one or two variables Question, Answer Explained

Math · AlgebraEasy

Which of the following represents all solutions to the inequality $-2 \le x - 5 < 3$ ?

$-7 \le x < -2$

$x \ge 3$

$-2 \le x < 8$

$3 \le x < 8$

Show answer and explanation

Answer: D

Add $5$ to all three parts of the compound inequality: $-2 + 5 \le x < 3 + 5$ , so $3 \le x < 8$ .

Choice A subtracts $5$ from each part instead of adding $5$ .

Why the other choices are wrong

A. This subtracts 5 from each part. To undo x - 5, add 5.
B. This keeps only the left part. The values of x must also satisfy x - 5 < 3, so x < 8.
C. This adds 5 only to the right part. Both parts must change by the same amount.

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