QuestionSolve the inequality $|m+6|+11 \leq 22$ . Choose the correct solution set: A, B, C, or D.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, $|m+6|$ is always non-negative. . We are trying to solve the inequality $|m+6| +11 \leq22$ .

STEP 2

First, we need to isolate the absolute value on one side of the inequality. We can do this by subtracting11 from both sides.
$|m+6| +11 -11 \leq22 -11$

STEP 3

implify the inequality.
$|m+6| \leq11$

STEP 4

The absolute value inequality $|m+6| \leq11$ can be rewritten as a compound inequality without absolute value $-11 \leq m+6 \leq11$ .

STEP 5

Now, we need to isolate $m$ in the compound inequality. We can do this by subtracting from all parts of the inequality.
$-11 - \leq m+ - \leq11 -$

STEP 6

implify the inequality.
$-17 \leq m \leq5$ The solution set is $\{m \mid-17\leq m\leq5\}$ . This matches with option A. The solution set is $\{m \mid-17<m<5\}$ if we exclude the boundary points -17 and5. However, since the original inequality includes the equal sign, we should include the boundary points in the solution set.

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