Question

Need help haven’t been able to get this question right for while

Answer 1

Explanation

Absolute value basically measures how far the number is from zero,for example

$\lvert x\rvert$

as we can see

$\lvert x\rvert=\lvert-x\rvert$

hence,

Step 1

$\lvert x\rvert=0$

so, we need to find a number such the distance from zero to that number be zero,

therefore , that number is zero

hence

$\begin{gathered} x_1=0 \\ x_2=0 \end{gathered}$

Step 2

$\lvert x\rvert=2$

now, weed to find a value such distance from zero is 2, so those values are +2 and -2

$\begin{gathered} x_1=2 \\ x_2=-2 \end{gathered}$

Step 3

c)

$\lvert x\rvert=-6$

the solution of a absolute value function is always positive, remeber we are talking about a distance, so, there is not solutioni

$\begin{gathered} c) \\ x_1=DNE \\ x_2=\text{DNE} \end{gathered}$

I hope this helps you