Chapter 8, Problem 55CR

To determine

Solve the inequality $-4g-5\ge -17$ and check your solutions.

Answer to Problem 55CR

  $g\le 3$

Explanation of Solution

Given:

The inequality, $-4g-5\ge -17$

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 $-4g-5\ge -17$ , first isolate the variable term on left side by performing some basic operations. Here to isolate g, first add $5$ both sides and then divide both sides by $-4$ and simplify further to get

  $\begin{array}{c}-4g-5\ge -17\\ -4g-5+5\ge -17+5\\ -4g\ge -12\\ \frac{-4g}{-4}\ge \frac{-12}{-4}\\ g\le 3\end{array}$

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

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

  $\begin{array}{c}-4g-5\ge -17\\ -4\left(2\right)-5\ge -17\\ -8-5\ge -17\\ -13\ge -17\text{True statement}\end{array}$

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