To solve the inequality [tex]\(-3t \geq 39\)[/tex] for [tex]\(t\)[/tex], follow these steps:
1. Identify the inequality:
The given inequality is:
[tex]\[
-3t \geq 39
\][/tex]
2. Isolate the variable [tex]\(t\)[/tex]:
To isolate [tex]\(t\)[/tex], we need to divide both sides of the inequality by -3. It's important to remember that when you divide or multiply both sides of an inequality by a negative number, you must reverse the direction of the inequality.
3. Divide both sides by -3:
[tex]\[
t \leq \frac{39}{-3}
\][/tex]
4. Simplify the fraction:
Calculate the value of [tex]\(\frac{39}{-3}\)[/tex]:
[tex]\[
\frac{39}{-3} = -13
\][/tex]
5. Write the final inequality:
After simplification, the inequality is:
[tex]\[
t \leq -13
\][/tex]
So, the solution to the inequality [tex]\(-3t \geq 39\)[/tex] is:
[tex]\[
t \leq -13
\][/tex]
