Question

In the following equations, 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)$Nosolution$

(c)$z=0$

Step-by-step solution

 Part (a) Step 1: Given information

$\left|x\right|=6$

 Part (a) Step 2: Calculation

The equivalent equations are

$$\begin{gathered} x=-6orx=6 \\ \Rightarrow x=\pm 6 \end{gathered}$$

 Part (b) Step 1: Given information

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

 Part (b) Step 2: Calculation

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

Part (c) Step 1: Given information

$\left|z\right|=0$

 Part (c) Step 2: Calculation

The equivalent equations are

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

The required solutions are

(a) $x=\pm 6$

(b) No solution

(c)$z=0$