Answer :

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.