Solve the inequality algebraically. Write the solution in interval notation.
-$\left| \frac { x - 5 } { 4 } \right| \leq 2$
A) $( - \infty , - 3 ) \cup ( 13 , \infty )$
B) $( - \infty , - 3 ] \cup [ 13 , \infty )$
C) $[ - 3,13 ]$
D) $( - 3,13 )$

Question

Quizplus · Accepted Answer

To solve the inequality $\left| \frac { x - 5 } { 4 } \right| \leq 2$, we remove the absolute value and solve the two resulting inequalities: $\frac { x - 5 } { 4 } \leq 2$ and $\frac { x - 5 } { 4 } \geq -2$. Solving these gives $x \leq 13$ and $x \geq -3$, respectively. Combining these gives the solution $[ - 3,13 ]$.

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Solve the Inequality Algebraically $\left| \frac { x - 5 } { 4 } \right| \leq 2$