Which of the following is the solution to the inequality 2x -... | SAT Linear inequalities in one or two variables Question, Answer Explained

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Which of the following is the solution to the inequality $\frac{2x - 1}{3} \ge x + 2$ ?

$x \le -7$

$x \ge -7$

$x \le -3$

$x \ge 7$

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Answer: A

Multiply both sides by $3$ : $2x - 1 \ge 3x + 6$ . Subtract $3x$ from both sides and add $1$ to both sides: $-x \ge 7$ . Multiply both sides by $-1$ and reverse the inequality: $x \le -7$ .

Choice B forgets to reverse the inequality sign when multiplying both sides by $-1$ .

Why the other choices are wrong

B. This forgets to reverse the inequality sign when dividing both sides by -1.
C. This multiplies x by 3 but not the 2. Both terms of x + 2 must be multiplied by 3.
D. This drops a negative sign. From -x ≥ 7, the solution is x ≤ -7.

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