Let's solve the inequality [tex]\( -4t - 5 > 2t + 13 \)[/tex] for [tex]\( t \)[/tex].
### Step-by-Step Solution:
1. Move all terms involving [tex]\( t \)[/tex] to one side of the inequality.
To do this, we should subtract [tex]\( 2t \)[/tex] from both sides:
[tex]\[
-4t - 5 - 2t > 2t + 13 - 2t
\][/tex]
Simplifying the terms, we get:
[tex]\[
-6t - 5 > 13
\][/tex]
2. Move the constant term to the other side of the inequality.
To isolate the term involving [tex]\( t \)[/tex], we add 5 to both sides:
[tex]\[
-6t - 5 + 5 > 13 + 5
\][/tex]
Simplifying the constants, we get:
[tex]\[
-6t > 18
\][/tex]
3. Isolate [tex]\( t \)[/tex] by dividing both sides by the coefficient of [tex]\( t \)[/tex].
Since the coefficient of [tex]\( t \)[/tex] is -6, we divide both sides of the inequality by -6. Remember that dividing by a negative number reverses the inequality sign:
[tex]\[
\frac{-6t}{-6} < \frac{18}{-6}
\][/tex]
Simplifying this, we obtain:
[tex]\[
t < -3
\][/tex]
Therefore, the solution to the inequality [tex]\( -4t - 5 > 2t + 13 \)[/tex] is [tex]\( t < -3 \)[/tex].
In the list of provided options, the correct one is:
[tex]\[ t < -3. \][/tex]
