Let's solve the inequality step by step and find the solution set.
Given inequality:
[tex]\[ 5x + 38 \leq 4(2 - 5x) \][/tex]
First, distribute the 4 on the right side:
[tex]\[ 5x + 38 \leq 8 - 20x \][/tex]
Next, let's move all terms involving [tex]\(x\)[/tex] to one side and constant terms to the other side. We can start by adding [tex]\(20x\)[/tex] to both sides:
[tex]\[ 5x + 20x + 38 \leq 8 \][/tex]
[tex]\[ 25x + 38 \leq 8 \][/tex]
Subtract 38 from both sides to isolate the [tex]\(x\)[/tex] term:
[tex]\[ 25x \leq 8 - 38 \][/tex]
[tex]\[ 25x \leq -30 \][/tex]
Finally, divide both sides by 25 to solve for [tex]\(x\)[/tex]:
[tex]\[ x \leq \frac{-30}{25} \][/tex]
[tex]\[ x \leq -\frac{6}{5} \][/tex]
[tex]\[ x \leq -1.2 \][/tex]
The solution set for the inequality is:
[tex]\[ x \leq -1.2 \][/tex]
To determine the correct graph representing this solution set, we look for the graph where:
1. The line is at [tex]\( x = -1.2 \)[/tex].
2. The shaded region includes all values less than or equal to [tex]\(-1.2\)[/tex].
Without the graphs provided, one would look for the graph that meets these conditions. The correct graph should have a solid line at [tex]\( x = -1.2 \)[/tex] (indicating [tex]\(\leq\)[/tex]) and shading to the left of the line.
Therefore, based on this analysis, the best graph is the one that represents [tex]\( x \leq -1.2 \)[/tex]. Please select the graph (A, B, C, or D) that appropriately indicates this solution set.
