Question

How do you solve `abs(t+6)=4`?

Answer 1

`t=-10" and " t=-2`

Explanation:

The value inside the `color(blue)"absolute value"` can be positive or negative but always produces a positive answer.

For example : `|-4|=4" and" |4|=4`

The absolute value informs us about how far the number is from the origin with no consideration of it's direction.

`- 4 and + 4 " are both 4 units from the origin."`

This is also true for algebraic expressions inside the absolute value bars, so

`t+6=4rArrt=4-6rArrt=-2`

and

`-(t+6)=4rArr-t-6=4`

add 6 to both sides.

`-tcancel(-6)cancel(+6)=4+6`

`rArr-t=10rArrt=-10`

Check : `t=-2rArr|-2+6|=|4|=4`

and `t=-10rArr|-10+6|=|-4|=4`

Thus solutions are t = - 10 and t = - 2