Question

Help with this math question

Answer 1

The given inequality is:

|-8x+24| \leq 16

This inequality can be divided in two parts as:

a) -16 \leq -8x +24

b) -8x + 24 \leq 16

Solving part a:

-16 \leq -8x+24 \\ \\ 
-40 \leq -8x \\ \\ 
5 \geq x \\ 
or \\ 
x \leq 5

Solving part b:

-8x+24 \leq 16 \\ \\ 
-8x \leq -8 \\ \\ 
x \geq 1

Therefore, the solution to the given inequality is x \leq 5 and x \geq 1. Combining both the ranges we get the solution: 1 \leq x \leq 5.

In interval notation, this solution can be expressed as [1,5

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Answer 2

The given inequality is:

$|-8x+24| \leq 16$

This inequality can be divided in two parts as:

a) $-16 \leq -8x +24$
b) $-8x + 24 \leq 16$

Solving part a:

$-16 \leq -8x+24 \\ \\ -40 \leq -8x \\ \\ 5 \geq x \\ or \\ x \leq 5$

Solving part b:

$-8x+24 \leq 16 \\ \\ -8x \leq -8 \\ \\ x \geq 1$

Therefore, the solution to the given inequality is $x \leq 5$ and $x \geq 1$. Combining both the ranges we get the solution: $1 \leq x \leq 5$.

In interval notation, this solution can be expressed as [1,5]