Chapter 8, Problem 57CR

To determine

Solve the inequality $24-3c\le 15$ and check your solutions

Answer to Problem 57CR

  $c\le 3$

Explanation of Solution

Given:

The inequality, $24-3c\le 15$

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
• Inequality sign get reverse on multiplying or dividing by a negative number

Calculation:

In order to solve the inequality $24-3c\le 15$ , first isolate the variable term on left side by performing some basic operations. Here to isolate c, first subtract $24$ both sides and then divide both sides by $-3$ and simplify further to get

  $\begin{array}{c}24-3c\le 15\\ 24-3c-24\le 15-24\\ -3c\ge -9\\ \frac{-3c}{-3}\ge \frac{-9}{-3}\\ c\le 3\end{array}$

Thus, the solution of the given inequality is $c\le 3$ .

Now in order to check the solution of the equation, substitute $c\le 3$ in the given equation and check whether the left hand side and right hand side are equal. So, it gives

  $\begin{array}{c}24-3c\le 15\\ 24-3\left(9\right)\le 15\\ 24-9\le 15\\ 15\le 15\text{True statement}\end{array}$

Thus, the solution of the given equation is $c\le 3$ .