Solve the inequality. $$\left| \frac { x + 5 } { 2 } \right| \geq 5$$
A) $[ - 15,5 ]$
B) $[ 15 , \infty )$
C) $( - \infty , - 15 ] \cup [ 5 , \infty )$
D) $( - \infty , - 15 ) \cup ( 5 , \infty )$
E) $\varnothing$

Question

Quizplus · Accepted Answer

To solve the inequality $\left| \frac { x + 5 } { 2 } \right| \geq 5$, we consider two cases due to the absolute value:1. $\frac { x + 5 } { 2 } \geq 5$Solving for $x$, we multiply both sides by 2: $x + 5 \geq 10$, which simplifies to $x \geq 5$.2. $\frac { x + 5 } { 2 } \leq -5$Similarly, multiplying both sides by 2 gives: $x + 5 \leq -10$, simplifying to $x \leq -15$.Combining these two cases, we get $x \leq -15$ or $x \geq 5$, which is represented by the union of two intervals: $( - \infty , - 15 ] \cup [ 5 , \infty )$.

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Solve the Inequality $\left| \frac { x + 5 } { 2 } \right| \geq 5$