Chapter 1.5, Problem 17PPSE

Solution

To solve the inequality $57-4t\ge 13$ and graph the solution.

  $a>11$

The graph of solution set is shown below:

  

Given:

The inequality, $57-4t\ge 13$ .

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$ , then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$ , then use a bracket $\left[\right]$ on the interval
• To graph the endpoint with strict inequality $<\text{ or}>$ , use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$ , use the bracket or a solid circle at that endpoint.
• Multiplying or dividing an inequality by a negative number reverse the inequality sign.

Calculation:

In order to solve the given inequality $57-4t\ge 13$ , perform the basic algebraic operations to isolate the variable term as shown below

  $\begin{array}{c}57-4t\ge 13\\ 57-57-4t\ge 13-57\\ -4t\ge -44\\ \frac{-4t}{-4}\le \frac{-44}{-4}\\ t\le 11\end{array}$

Thus, the solution of the given inequality is $t\le 11$ .

Since the inequality sign is not strict, use a solid circle at $11$ and move toward left on the number line as shown below