Exercise 66 Page 303

Inequalities can be solved in the same way as equations, by performing inverse operations on both sides until the variable is isolated. The only difference is that when you divide or multiply by a negative number, you must reverse the inequality sign. This tells us that all values greater than or equal to $45$ satisfy the inequality. Knowing this, let's write the solution set.

Checking Our Solution

We can check our solution by substituting a few arbitrary values into the given inequality. The value satisfies the inequality if the inequality remains true after substituting and simplifying.

$t$	$\text{-}\frac{2}{3}t\le \text{-}30$	Evaluate
$42$	$\text{-}\frac{2}{3}(42)\le \text{-}30$	$\text{-}28\nleqq \text{-}30$
$45$	$\text{-}\frac{2}{3}(45)\le \text{-}30$	$\text{-}30\le \text{-}30$
$48$	$\text{-}\frac{2}{3}(48)\le \text{-}30$	$\text{-}32\le \text{-}30$

We can conclude that, as long as $t$ is greater than or equal to $45,$ the inequality is satisfied. This means our solution is correct.