Question $5|x-7|+8 \leq 43$

Studdy Solution

STEP 1

1. The inequality involves an absolute value expression.
2. We need to solve for $x$ such that the inequality holds true.
3. The absolute value inequality can be split into two separate inequalities.

STEP 2

1. Isolate the absolute value expression.
2. Split the absolute value inequality into two separate inequalities.
3. Solve each inequality for $x$ .
4. Combine the solutions to find the overall solution for $x$ .

STEP 3

First, isolate the absolute value expression $|x-7|$ in the inequality:
$5|x-7| + 8 \leq 43$
Subtract 8 from both sides to isolate the term with the absolute value:
$5|x-7| \leq 35$

STEP 4

Divide both sides by 5 to further isolate the absolute value:
$|x-7| \leq 7$

STEP 5

Split the absolute value inequality into two separate inequalities:
$x-7 \leq 7 \quad \text{and} \quad x-7 \geq -7$

STEP 6

Solve each inequality for $x$ :
For $x-7 \leq 7$ :
$x \leq 14$
For $x-7 \geq -7$ :
$x \geq 0$

STEP 7

Combine the solutions to find the overall solution for $x$ :
The solution is the intersection of the two inequalities:
$0 \leq x \leq 14$
The solution to the inequality is $\boxed{0 \leq x \leq 14}$ .

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