To solve the inequality [tex]\( 5x - 8 \leq -38 \)[/tex], we need to isolate the variable [tex]\( x \)[/tex] by performing operations that will simplify the inequality step-by-step.
1. Initial Inequality:
[tex]\[
5x - 8 \leq -38
\][/tex]
2. Add 8 to both sides:
To get rid of the constant [tex]\(-8\)[/tex] on the left side, we add 8 to both sides of the inequality:
[tex]\[
5x - 8 + 8 \leq -38 + 8
\][/tex]
Simplifying both sides:
[tex]\[
5x \leq -30
\][/tex]
3. Divide both sides by 5:
To isolate [tex]\( x \)[/tex], we divide both sides of the inequality by the coefficient of [tex]\( x \)[/tex], which is 5:
[tex]\[
\frac{5x}{5} \leq \frac{-30}{5}
\][/tex]
Simplifying both sides:
[tex]\[
x \leq -6
\][/tex]
4. Solution:
The solution to the inequality [tex]\( 5x - 8 \leq -38 \)[/tex] is:
[tex]\[
x \leq -6
\][/tex]
Therefore, the inequality [tex]\( 5x - 8 \leq -38 \)[/tex] simplifies to [tex]\( x \leq -6 \)[/tex].
