To solve the inequality [tex]\(\frac{2t + 5}{3} < -9\)[/tex] for [tex]\(t\)[/tex], follow these steps:
1. Remove the fraction: To eliminate the fraction, multiply both sides of the inequality by 3:
[tex]\[
3 \cdot \frac{2t + 5}{3} < 3 \cdot (-9)
\][/tex]
Simplifying this, we get:
[tex]\[
2t + 5 < -27
\][/tex]
2. Isolate the term with [tex]\(t\)[/tex]: Subtract 5 from both sides of the inequality to isolate the term that contains [tex]\(t\)[/tex]:
[tex]\[
2t + 5 - 5 < -27 - 5
\][/tex]
Simplifying this, we get:
[tex]\[
2t < -32
\][/tex]
3. Solve for [tex]\(t\)[/tex]: Finally, divide both sides of the inequality by 2 to solve for [tex]\(t\)[/tex]:
[tex]\[
\frac{2t}{2} < \frac{-32}{2}
\][/tex]
Simplifying this, we get:
[tex]\[
t < -16
\][/tex]
Therefore, the solution to the inequality [tex]\(\frac{2t + 5}{3} < -9\)[/tex] is:
[tex]\[
t < -16
\][/tex]
