Chapter 1.7, Problem 22E

To determine

To calculate: The solution of the given inequality, $6x-4\le 2+8x$, and graph the solution set.

The solution set of the given inequality, $6x-4\le 2+8x$, is $x\ge -3$.

Calculation:

Consider the given inequality, $6x-4\le 2+8x$.

Subtract $8x$ from each part by using the property of addition of a constant to an inequality, according to which, if $a<b$, then $a<b$ becomes $a+c<b+c$.

$-2x-4\le 2$

Add 4 from each part by using the property of addition of a constant to an inequality, according to which, if $a<b$, then $a<b$ becomes $a+c<b+c$.

$-2x\le 6$

Divide each part by $-2$ by using the multiplicative property of an inequality, according to which, if $c>0$, then $a<b$ becomes $ac<bc$ and if $c<0$, then $a>b$ becomes $ac<bc$.

$x\le -3$

The solution set of the given inequality is the set of all real numbers that are equal to or less than $-3$ which can be denoted by $\left(-\infty ,-3\right]$.

Graph:

The solution set of the inequality is shown in the graph.

The bracket at $x=-3$ means that the value at $x=-3$ is included in the solution set of the given equation.