To solve the inequality:
[tex]\[
2(4 + 2x) \geq 5x + 5
\][/tex]
let's follow a step-by-step approach.
1. Expand the expression on the left side:
[tex]\[
2(4 + 2x) = 2 \cdot 4 + 2 \cdot 2x = 8 + 4x
\][/tex]
The inequality now becomes:
[tex]\[
8 + 4x \geq 5x + 5
\][/tex]
2. Isolate the variable [tex]\( x \)[/tex] on one side:
Subtract [tex]\( 4x \)[/tex] from both sides:
[tex]\[
8 + 4x - 4x \geq 5x + 5 - 4x
\][/tex]
Simplify the inequality:
[tex]\[
8 \geq x + 5
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
Subtract 5 from both sides to isolate [tex]\( x \)[/tex]:
[tex]\[
8 - 5 \geq x + 5 - 5
\][/tex]
Simplify:
[tex]\[
3 \geq x
\][/tex]
Or, equivalently:
[tex]\[
x \leq 3
\][/tex]
The solution to the inequality [tex]\( 2(4 + 2x) \geq 5x + 5 \)[/tex] is:
[tex]\[
x \leq 3
\][/tex]
So, the correct answer from the given options is:
[tex]\[
x \leq 3
\][/tex]
