Chapter 1, Problem 41SGR

To determine

To solve: the given inequality and graph the solution on number line.

Answer to Problem 41SGR

The solution is given by $x\le -\frac{2}{9}$ .

Explanation of Solution

Given information:

Given inequality

  $4-7x\ge 2\left(x+3\right)$

Calculation:

Consider the given inequality,

  $4-7x\ge 2\left(x+3\right)$

Now, solve the inequality as shown,

  $\begin{array}{c}4-7x\ge 2\left(x+3\right)\\ 4-7x\ge 2x+6\\ 4-7x-2x\ge 2x+6-2x\\ 4-9x\ge 6\\ 4-9x-4\ge 6-4\\ -9x\ge 2\\ \frac{-9x}{-9}\le \frac{2}{-9}\\ x\le -\frac{2}{9}\end{array}$

Now, graph the inequality as shown:

  

The closed ball suggests that the solution region is included the point $-\frac{2}{9}$ .

Lesser than sign indicates the solution region is left side to the point $-\frac{2}{9}$ on number line.

Hence, the solution of the inequality is $x\le -\frac{2}{9}$ .