Question

Solve (a) $\left|x\right|=2$

(b) $\left|y\right|=-4$

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

Short answer

The required solution: (a) $x_1=-2,x_2=2$

(b) No solution

(c)$z=0$

Step-by-step solution

Step 1. Given information.

The given functions are:

(a) $\left|x\right|=2$

(b) $\left|y\right|=-4$

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

Part (a) Step 1. Solve   

We have:

$\left|x\right|=2$

Apply absolute rule: $\mathrm{If}\hspace{0.17em}\left|u\right|\hspace{0.17em}=\hspace{0.17em}a,\hspace{0.17em}a>0\hspace{0.17em}\mathrm{then}\hspace{0.17em}u\hspace{0.17em}=\hspace{0.17em}a\hspace{0.17em}\mathrm{or}\hspace{0.17em}u\hspace{0.17em}=\hspace{0.17em}-a$

$x=2$or$x=-2$

Part (b) Step 1. Solve. 

We have:

$\left|y\right|=-4$

Absolute value can not be less than $0.$

Hence, no solution for$y\in R.$

Part (c) Step 1. Solve  

We have:

$\left|z\right|=0$

Apply absolute rule: If $\left|u\right|=0$then $u=0$

$z=0$