Sure, let's solve the given inequality step by step:
The given inequality is:
[tex]\[ 12 \leq \frac{x}{4} + 8 \leq 20 \][/tex]
### Step 1: Isolate [tex]\(\frac{x}{4}\)[/tex]
First, we'll subtract 8 from all parts of the inequality to isolate [tex]\(\frac{x}{4}\)[/tex].
[tex]\[ 12 - 8 \leq \frac{x}{4} + 8 - 8 \leq 20 - 8 \][/tex]
Simplifying, we get:
[tex]\[ 4 \leq \frac{x}{4} \leq 12 \][/tex]
### Step 2: Solve for [tex]\(x\)[/tex]
Next, we'll multiply all parts of the inequality by 4 to solve for [tex]\(x\)[/tex].
[tex]\[ 4 \times 4 \leq \frac{x}{4} \times 4 \leq 12 \times 4 \][/tex]
Simplifying, we get:
[tex]\[ 16 \leq x \leq 48 \][/tex]
Thus, the solution to the inequality [tex]\(12 \leq \frac{x}{4} + 8 \leq 20\)[/tex] is:
[tex]\[ 4 \leq \frac{x}{4} \leq 12 \][/tex]
and
[tex]\[ 16 \leq x \leq 48 \][/tex]
So, the values of [tex]\(x\)[/tex] that satisfy the inequality are between 16 and 48, inclusive.
