Question

In the following exercises,solve

(a)$\left|x\right|=6$

(b $\left|-y\right|=-3$

(c)$\left|z\right|=0$

Short answer

The required solutions are

(a) $x=\pm 6$

(b) No Solutions

(c)$z=0$

Step-by-step solution

(a) STEP 1: Given information

$\left|x\right|=6$

(a) STEP 2: Calculation

The equivalent equations are

$x=-6orx=6$

$\Rightarrow x=\pm 6$

(b) STEP 1: Given information 

$\left|y\right|=-3$

(b) STEP 2: Calculation

No solution, since an absolute value is always positive, there are no solutions to this equation.

(c) STEP 1: Given equation

$\left|z\right|=0$

(c) STEP 2:Calculation

$$\begin{gathered} \left|z\right|=0 \\ z=-0orz=0 \\ Since-0=0 \end{gathered}$$

So there is only solution