To determine which graph represents the solution set for the inequality [tex]\(5x + 38 \leq 4(2 - 5x)\)[/tex], we need to solve the inequality step-by-step.
1. Start with the given inequality:
[tex]\[
5x + 38 \leq 4(2 - 5x)
\][/tex]
2. Distribute the 4 on the right side:
[tex]\[
4(2 - 5x) = 8 - 20x
\][/tex]
So the inequality becomes:
[tex]\[
5x + 38 \leq 8 - 20x
\][/tex]
3. Combine like terms by adding [tex]\(20x\)[/tex] to both sides:
[tex]\[
5x + 20x + 38 \leq 8 - 20x + 20x
\][/tex]
[tex]\[
25x + 38 \leq 8
\][/tex]
4. Isolate the term with [tex]\(x\)[/tex] on one side by subtracting 38 from both sides:
[tex]\[
25x + 38 - 38 \leq 8 - 38
\][/tex]
[tex]\[
25x \leq -30
\][/tex]
5. Solve for [tex]\(x\)[/tex] by dividing both sides by 25:
[tex]\[
x \leq -30 / 25
\][/tex]
6. Simplify the fraction:
[tex]\[
x \leq -6 / 5
\][/tex]
[tex]\[
x \leq -1.2
\][/tex]
Therefore, the solution set for the inequality [tex]\(5x + 38 \leq 4(2 - 5x)\)[/tex] is [tex]\(x \leq -1.2\)[/tex].
The graph that represents this solution set will show a number line with a closed circle at [tex]\(x = -1.2\)[/tex] (indicating that -1.2 is included in the solution set) and shading to the left of -1.2 (indicating all values less than or equal to -1.2 are part of the solution set).
Select the graph that matches the description above.
