Question

Question 13 only, I inserted a picture. Please show your work. graph the solution to the in equality

Answer 1

`(-\infty,-3\rbrack\cup\lbrack3,\infty)`

Step-by-step explanation

`\begin{gathered} x^2\ge9 \\ \end{gathered}`

An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from 0 on the number line

Step 1

solve the inequality

`\begin{gathered} x^2\ge9 \\ \text{square root in both sides} \\ √(x^2)\ge√(9) \\ x\ge\pm3 \\ so \\ \lvert x\rvert\ge3 \\ \text{two cases} \\ x\ge3\text{ and x}\leq-3 \end{gathered}`

so, in intervals

`(-\infty,-3\rbrack\cup\lbrack3,\infty)`

Step 2

graph the solution

`(-\infty,-3\rbrack\cup\lbrack3,\infty)`

I hope this helps you