To find the solution to the inequality [tex]\( 8(x - 5) - 3x \geq -20 \)[/tex], follow these steps:
1. Distribute the 8 inside the parentheses:
[tex]\[
8(x - 5) = 8x - 40
\][/tex]
So the inequality becomes:
[tex]\[
8x - 40 - 3x \geq -20
\][/tex]
2. Combine like terms:
[tex]\[
8x - 3x - 40 \geq -20
\][/tex]
Simplifying this, we get:
[tex]\[
5x - 40 \geq -20
\][/tex]
3. Isolate the [tex]\( x \)[/tex] term by adding 40 to both sides:
[tex]\[
5x - 40 + 40 \geq -20 + 40
\][/tex]
Which simplifies to:
[tex]\[
5x \geq 20
\][/tex]
4. Solve for [tex]\( x \)[/tex] by dividing both sides by 5:
[tex]\[
x \geq \frac{20}{5}
\][/tex]
Which gives us:
[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]. Therefore, the correct answer is:
C. [tex]\( x \geq 4 \)[/tex]
