To solve the inequality [tex]\(8\left(\frac{x}{4} - 6\right) \geq 4\)[/tex], follow these steps:
1. Distribute the 8 within the parentheses:
[tex]\[
8 \cdot \left(\frac{x}{4}\right) - 8 \cdot 6 \geq 4
\][/tex]
Simplifying inside the parentheses:
[tex]\[
2x - 48 \geq 4
\][/tex]
This is because [tex]\(8 \cdot \frac{x}{4} = 2x\)[/tex] and [tex]\(8 \cdot 6 = 48\)[/tex].
2. Isolate the term involving [tex]\(x\)[/tex]:
To do this, add 48 to both sides of the inequality:
[tex]\[
2x - 48 + 48 \geq 4 + 48
\][/tex]
Simplifying the equation:
[tex]\[
2x \geq 52
\][/tex]
3. Solve for [tex]\(x\)[/tex]:
Finally, divide both sides of the inequality by 2:
[tex]\[
\frac{2x}{2} \geq \frac{52}{2}
\][/tex]
Simplifying:
[tex]\[
x \geq 26
\][/tex]
Therefore, the solution to the inequality is [tex]\(x \geq 26\)[/tex], which corresponds to option D.
So the correct answer is:
D. [tex]\(x \geq 26\)[/tex]
