Question

In the following exercises, solve

(a) $\left|x\right|=3$

(b) $\left|y\right|=-1$

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

Short answer

The required solution is

(a) $x=\pm 3$

(b) No solution

(c)$z=0$

Step-by-step solution

Part (a) Step 1: Given information

$\left|x\right|=3$

Step 2:Calculation

The equivalent equations are

$$\begin{gathered} x=-3orx=3 \\ \Rightarrow x=\pm 3 \end{gathered}$$

Part (b) Step 1 : Given information

$\left|y\right|=-1$

Part (b)  Step 2: Calculation

No solution, since an absolute value is always positive.

Part (c) Step 1: Given information

$\left|z\right|=0$

Part (c) Step 2: Calculation

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