Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $- 12 \leq \frac { 25 - 7 x } { 2 } \leq 12$
A) $[ 7 , \infty )$
B) $\left[ \frac { 1 } { 7 } , \infty \right)$
C) $\left( - \infty , \frac { 1 } { 7 } \right]$
D) $\left[ \frac { 1 } { 7 } , 7 \right]$
E) $\varnothing$

Question

Solve the compound inequality. Graph the solution set (if one exists) and write it using interval notation. $- 12 \leq \frac { 25 - 7 x } { 2 } \leq 12$
A) $[ 7 , \infty )$ 
B) $\left[ \frac { 1 } { 7 } , \infty \right)$ 
C) $\left( - \infty , \frac { 1 } { 7 } \right]$ 
D) $\left[ \frac { 1 } { 7 } , 7 \right]$ 
E) $\varnothing$

Quizplus · Accepted Answer

We begin by isolating the variable in the middle of the compound inequality:
$$
- 12 \leq \frac { 25 - 7 x } { 2 } \leq 12
$$
$$
- 24 \leq 25 - 7 x \leq 24
$$
$$
- 49 \leq - 7 x \leq - 1
$$
$$
7 \geq x \geq \frac{1}{7}
$$
This means that the solution set is the interval $\left[\frac{1}{7},7\right]$, so the correct answer is D.

Solve the Compound Inequality −12≤25−7x2≤12- 12 \leq \frac { 25 - 7 x } { 2 } \leq 12−12≤225−7x​≤12

Solve the Compound Inequality $- 12 \leq \frac { 25 - 7 x } { 2 } \leq 12$