To solve the inequality [tex]\( 8(x-5) - 3x \geq -20 \)[/tex], follow these steps:
1. Distribute the 8 across the term [tex]\((x-5)\)[/tex]:
[tex]\[
8(x-5) - 3x \geq -20
\][/tex]
becomes:
[tex]\[
8x - 40 - 3x \geq -20
\][/tex]
2. Combine like terms on the left-hand side:
[tex]\[
(8x - 3x) - 40 \geq -20
\][/tex]
simplifies to:
[tex]\[
5x - 40 \geq -20
\][/tex]
3. Add 40 to both sides of the inequality to isolate the term with [tex]\(x\)[/tex]:
[tex]\[
5x - 40 + 40 \geq -20 + 40
\][/tex]
simplifies to:
[tex]\[
5x \geq 20
\][/tex]
4. Divide both sides by 5 to solve for [tex]\(x\)[/tex]:
[tex]\[
\frac{5x}{5} \geq \frac{20}{5}
\][/tex]
simplifies to:
[tex]\[
x \geq 4
\][/tex]
Thus, the solution set of the inequality [tex]\( 8(x-5) - 3x \geq -20 \)[/tex] is:
[tex]\[
x \geq 4
\][/tex]
So the correct answer is:
A. [tex]\( x \geq 4 \)[/tex]
