Chapter 2.5, Problem 30S

To determine

Solve the equation.

Answer to Problem 30S

  $\boxed{x=5}$ Or $\boxed{x=-1}$

Explanation of Solution

Given information:

Solve each equation.

  $-4\left|x-2\right|=-12$

Calculation:

For any real number $x$ the absolute value or modulus of $x$ is denoted by $\left|x\right|$ ( a vertical bar on each side of the quantity) and is defined as

  $\left|x\right|=\{\begin{array}{l}x,if,x\ge 0\\ -x,if,x<0\end{array}$

Consider the following expression:

  $-4\left|x-2\right|=-12$

Divide both sides by $-4$ and Simplify;

  $\frac{-4\left|x-2\right|}{-4}=\frac{-12}{-4}$

  $\left|x-2\right|=3$

Apply definition of the absolute value.

  $\left(x-2\right)=3$

Add both sides by $2$ and simplify;

  $x-2+2=3+2$

  $x=5$

Hence, $x=5$

$-\left(x-2\right)=3$

Subtract both sides by $2$and Simplify;

  $-x+2-2=3-2$

  $-x=1$

  $x=-1$

Hence, $x=-1$Hence, the answer is $\boxed{x=5}$or $\boxed{x=-1}$