Sure, let's solve the inequality:
[tex]\[
\frac{t}{-3.2} < 5
\][/tex]
First, we need to isolate [tex]\( t \)[/tex]. To do this, we'll multiply both sides of the inequality by [tex]\(-3.2\)[/tex].
However, we need to remember an important rule when working with inequalities: when you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign reverses.
So, let's multiply both sides by [tex]\(-3.2\)[/tex]:
[tex]\[
t > 5 \cdot -3.2
\][/tex]
Next, we perform the multiplication on the right-hand side:
[tex]\[
5 \cdot -3.2 = -16
\][/tex]
So our inequality now becomes:
[tex]\[
t > -16
\][/tex]
Therefore, the solution to the inequality [tex]\(\frac{t}{-3.2} < 5\)[/tex] is:
[tex]\[
t > -16
\][/tex]
