Chapter 8, Problem 56CR

To determine

Solve the inequality $18>-12+6m$ and check your solutions

Answer to Problem 56CR

  $g\le -3$

Explanation of Solution

Given:

The inequality, $18>-12+6m$

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 $18>-12+6m$ , first isolate the variable term on left side by performing some basic operations. Here to isolate m, first add $12$ both sides and then divide both sides by $6$ and simplify further to get

  $\begin{array}{c}18>-12+6m\\ 18+12>-12+6m+12\\ 30\ge 6m\\ \frac{30}{6}\ge \frac{6m}{6}\\ 5\ge m\end{array}$

Thus, the solution of the given inequality is $5\ge m$ .

Now in order to check the solution of the equation, substitute $5\ge m$ in the given equation and check whether the left hand side and right hand side are equal. So, it gives

  $\begin{array}{c}18>-12+6m\\ 18>-12+6\left(4\right)\\ 18\ge -12+24\\ 18\ge 12\text{True statement}\end{array}$

Thus, the solution of the given equation is $5\ge m$ .