Question

How do you solve `|3x+8|+2=7`?

Answer 1

`x=-1,x=-13/3`

Explanation:

`color(orange)"Reminder"`

|5| = 5 and |- 5| = 5

The`color(magenta)" absolute value of both 5 and -5 is 5"`

This is because the absolute value is a measure of how far a value is from the origin , but doesn't consider direction. -5 and 5 are both 5 units from the origin.

However, when there are variables inside the 'bars' we don't know if the value is positive or negative and so must consider both options.

Thus for |3x + 8 | + 2 = 7

We must consider `color(red)"3x+8+2=7"`

and `color(blue)"-(3x+8)+2=7"`

`rArrcolor(red)"3x=7-2-8"tocolor(red)"3x=-3" tocolor(red)"x=-1"`

`rArrcolor(blue)"-3x-8+2=7"tocolor(blue)"-3x=7-2+8"tocolor(blue)"x=-13/3"`