Chapter 6.4, Problem 54S

To determine

To solve: The inequality $-6x-8\ge -4$ using graph.

Answer to Problem 54S

The solution is $x\le -\frac{2}{3}$ .

Explanation of Solution

Given:

The inequality is $-6x-8\ge -4$ .

Calculation:

The corresponding equation of inequality is $-6x-8=-4$ . Solve $-6x-8=-4$ as follows:

  $\begin{array}{c}-6x-8=-4\\ -6x=-4+8\\ x=-\frac{4}{6}\\ x=-\frac{2}{3}\end{array}$

Consider a test point as $\left(0,0\right)$ in equality $-6x-8\ge -4$ as,

  $\begin{array}{r}-6\left(0\right)-8\stackrel{?}{\ge }4\\ 0-8\stackrel{?}{\ge }4\\ -8\stackrel{?}{\ge }4\end{array}$

Since $-8$ is not greater than 4, therefore, shade the plane that does not contain $\left(0,0\right)$ .

For the inequality $-6x-8\ge -4$ , shade towards the left of the line $-6x-8=-4$ . Graph the inequality $-6x-8\ge -4$ as shown below:

  

Thus, the solution is $x\le -\frac{2}{3}$ .