Question

Due Thu 06/16/2Solve the following inequalities and match them with the graphs of their solution sets, if they exist.(a,b,c) lxl <= -9 A. No solution (a,b,c) lxl <= 9 (a,b,c) lxl >= -9

Answer 1

The Solution:

Given:

We are required to solve each of the above inequalities.

Apply the Modulus Inequality Theorem below:

`\begin{gathered} \left|x\right|\le -9 \\ Absolute\text{ value cannot be less than 0.} \\ So,\left|x\right|\le-9\text{ has no solution.} \end{gathered}`

Thus, the correct answer is [option A]

For the inequality below:

`\begin{gathered} \left|x\right|\le 9 \\ By\text{ the Absolute value rule:} \\ |u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a \end{gathered}`
`\begin{gathered} \left|x\right|\le 9 \\ This\text{ becomes:} \\ -9\le \:x\le \:9 \\ Thus,\text{ the correct answer is \lbrack option B\rbrack} \end{gathered}`

For the third inequality:

`\left|x\right|\ge -9`

Apply the rule below:

So,

`\begin{gathered} \left|x\right|\ge -9 \\ \\ This\text{ becomes:} \\ x\leq-9 \\ or \\ x\ge9 \\ This\text{ means the solution is true for all values of x.} \end{gathered}`

Thus, the correct answer is [option C]