To solve the inequality [tex]\( 5x + 13 \geq -37 \)[/tex], follow these steps:
1. Isolate the variable term: Start by isolating the term involving [tex]\( x \)[/tex] on one side of the inequality.
[tex]\[
5x + 13 \geq -37
\][/tex]
2. Subtract 13 from both sides: To isolate the term with [tex]\( x \)[/tex], subtract 13 from both sides of the inequality.
[tex]\[
5x + 13 - 13 \geq -37 - 13
\][/tex]
Simplifying this, we get:
[tex]\[
5x \geq -50
\][/tex]
3. Divide by 5: To solve for [tex]\( x \)[/tex], divide both sides of the inequality by 5.
[tex]\[
\frac{5x}{5} \geq \frac{-50}{5}
\][/tex]
Simplifying this, we obtain:
[tex]\[
x \geq -10
\][/tex]
So the solution set for the inequality [tex]\( 5x + 13 \geq -37 \)[/tex] is:
[tex]\[
x \geq -10
\][/tex]
