Solve the inequality algebraically. Write the solution in interval notation.
-$$\left| \frac { x + 3 } { 2 } \right| \geq 1$$
A) $( - 5 , - 1 )$
B) $( - \infty , - 1 )$
C) $( - \infty , - 5 )$
D) $( - \infty , - 5 ] \cup [ - 1 , \infty )$

Question

Quizplus · Accepted Answer

To solve the inequality $\left| \frac { x + 3 } { 2 } \right| \geq 1$, we consider two cases due to the absolute value:1. $\frac { x + 3 } { 2 } \geq 1$Solving for $x$, we get $x + 3 \geq 2$, which simplifies to $x \geq -1$.2. $\frac { x + 3 } { 2 } \leq -1$Solving for $x$, we get $x + 3 \leq -2$, which simplifies to $x \leq -5$.Combining these two cases, the solution is $x \leq -5$ or $x \geq -1$, which in interval notation is $( - \infty , - 5 ] \cup [ - 1 , \infty )$.

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Solve the Inequality Algebraically $\left| \frac { x + 3 } { 2 } \right| \geq 1$