To determine the solution set of the given inequality [tex]\(8(x-5) - 3x \geq -20\)[/tex], follow these steps:
1. Distribute and combine like terms:
Start with the inequality:
[tex]\[
8(x-5) - 3x \geq -20
\][/tex]
First, distribute the 8 through the term [tex]\( (x-5) \)[/tex]:
[tex]\[
8x - 40 - 3x \geq -20
\][/tex]
2. Combine like terms:
Combine the [tex]\(x\)[/tex] terms on the left side:
[tex]\[
(8x - 3x) - 40 \geq -20
\][/tex]
Simplify it to:
[tex]\[
5x - 40 \geq -20
\][/tex]
3. Isolate the variable [tex]\(x\)[/tex]:
Add 40 to both sides of the inequality to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
5x - 40 + 40 \geq -20 + 40
\][/tex]
Simplify this to:
[tex]\[
5x \geq 20
\][/tex]
4. Solve for [tex]\(x\)[/tex]:
Divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
x \geq \frac{20}{5}
\][/tex]
Simplify the division:
[tex]\[
x \geq 4
\][/tex]
Conclusively, the solution set for the inequality [tex]\(8(x-5) - 3x \geq -20\)[/tex] is:
[tex]\[
x \geq 4
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{B. \, x \geq 4}
\][/tex]
