QuestionSolve the inequality $|m+6|+11 \leq 22$ and select the correct solution set format.

Studdy Solution

STEP 1

Assumptions1. The absolute value of a number is its distance from zero on the number line, and is always non-negative. . The inequality $|m+6|+11 \leq22$ is given.

STEP 2

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

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 solve the compound inequality for $m$ . 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 $\{m \mid -17 \leq m \leq5\}$ , which corresponds to option A. The solution set is $\{m \mid -17 \leq m \leq5\}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms