Question

Solve for x: 3|x − 3| + 2 = 14 (5 points)

x = 0, x = 7

x = −1, x = 7

No solutions

x = −1, x = 8.3

Answer 1

First, you need to get the absolute value on its own.
Subtract 2 on both sides.
3|x-3| = 12
Now divide by 3 on both sides and unfold the absolute value.
x-3 = 4 and x-3 = -4
Now solve both equations
Add 3 to both sides.
x = 1 and x = -1

Answer 2

`Solution, solve\:for\:x,\:3\left|x-3\right|+2=14\quad :\quad x=-1\quad \mathrm{or}\quad \:x=7`

`Steps:`

`\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}, 3\left|x-3\right|+2-2=14-2`

`\mathrm{Simplify}, 3\left|x-3\right|=12`

`\mathrm{Divide\:both\:sides\:by\:}3, (3\left|x-3\right|)/(3)=(12)/(3)`

`\mathrm{Simplify}, \left|x-3\right|=4`

`|f\left(x\right)|=a\quad \Rightarrow \:f\left(x\right)=-a\quad \mathrm{or}\quad \:f\left(x\right)=a, x-3=-4\quad \quad \mathrm{or}\quad \:\quad \:x-3=4`

`x-3=-4\quad :\quad x=-1`

`x-3=4\quad :\quad x=7`

`\mathrm{Combine\:the\:ranges}, x=-1\quad \mathrm{or}\quad \:x=7`

The correct answer is B. x=-1, x=7

Hope this helps!!!