Question

What is x when: |3x–1|=8

Answer 1

x=3 or/and x= -7/3

Explanation:

• 3x-1= 8

+1= +1

3x = 9

9 divided by 3 is x= 3

• 3x-1= -8

+1= +1

3x = -7

-7 divided by 3 is x= -7/3

Answer 2

`\huge\boxed{x=3\ \vee\ x=-(7)/(3)}`

Explanation:

`|a|=\left\{\begin{array}{ccc}a&\text{for}\ a\geq0\\-a&\text{for}\ a<0\end{array}\right\\\\|a|=k\to a=k\ \vee\ a=-k\ \text{for}\ k>0\\==========================\\\\|3x-1|=8\iff3x-1=8\ \vee\ 3x-1=-8\\\\\begin{array}{cccc}3x-1=8&\vee&3x-1=-8&\text{add 1 to both sides}\\3x-1+1=8+1&\vee&3x-1+1=-8+1\\3x=9&\vee&3x=-7&\text{divide both sides by 3}\\(3x)/(3)=(9)/(3)&\vee&(3x)/(3)=(-7)/(3)\\x=3&\vee&x=-(7)/(3)\\\end{array}`