To solve the inequality [tex]\(8(x - 5) - 3x \geq -20\)[/tex], let's go through the steps in a detailed manner:
1. Distribute the 8 across the terms inside the parenthesis:
[tex]\[
8(x - 5) - 3x \geq -20
\][/tex]
[tex]\[
8x - 40 - 3x \geq -20
\][/tex]
2. Combine like terms on the left-hand side:
[tex]\[
(8x - 3x) - 40 \geq -20
\][/tex]
[tex]\[
5x - 40 \geq -20
\][/tex]
3. Isolate the term with the variable [tex]\(x\)[/tex] by adding 40 to both sides of the inequality:
[tex]\[
5x - 40 + 40 \geq -20 + 40
\][/tex]
[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]
[tex]\[
x \geq 4
\][/tex]
Thus, the solution set for the inequality [tex]\(8(x - 5) - 3x \geq -20\)[/tex] is [tex]\(x \geq 4\)[/tex].
Among the given options:
- A. [tex]\(x \leq -12\)[/tex]
- B. [tex]\(x \geq 4\)[/tex]
- C. [tex]\(x \leq 12\)[/tex]
- D. [tex]\(x \geq -3\)[/tex]
The correct answer is:
B. [tex]\(x \geq 4\)[/tex]
