Chapter 8.8, Problem 61STP

To determine

What is the solution of this inequality $-4x+16\ge -4$

Answer to Problem 61STP

The solution of the inequality is $x\le 5$

Option J is correct

Explanation of Solution

Given:

The inequality, $-4x+16\ge -4$

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 mixed inequality $-4x+16\ge -4$ first isolate the variable term x by performing some basic operations. Here to isolate x terms on the left side, first subtract both sides by $16$ and then divide both sides by $-4$ and then Inequality sign get reverse on multiplying or dividing by a negative number and then simplify further as shown below:

  $\begin{array}{c}-4x+16\ge -4\\ -4x+16-16\ge -4-16\\ -4x\ge -20\\ \frac{-4x}{-4}\le \frac{-20}{-4}\\ x\le 5\end{array}$

Thus, the solution of the given inequality is $x\le 5$ .

Option J is correct