To solve the inequality [tex]\( 5y + 16 \leq 56 \)[/tex], we will follow these steps:
1. Isolate the term with the variable: We need to get [tex]\( 5y \)[/tex] by itself on one side of the inequality.
[tex]\[
5y + 16 \leq 56
\][/tex]
To isolate [tex]\( 5y \)[/tex], subtract 16 from both sides of the inequality:
[tex]\[
5y + 16 - 16 \leq 56 - 16
\][/tex]
Simplifying this, we get:
[tex]\[
5y \leq 40
\][/tex]
2. Solve for the variable: Now that we have [tex]\( 5y \leq 40 \)[/tex], we need to solve for [tex]\( y \)[/tex]. To do this, divide both sides of the inequality by 5:
[tex]\[
\frac{5y}{5} \leq \frac{40}{5}
\][/tex]
Simplifying this, we get:
[tex]\[
y \leq 8
\][/tex]
Therefore, the solution to the inequality [tex]\( 5y + 16 \leq 56 \)[/tex] is:
[tex]\[
y \leq 8
\][/tex]
