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

1 Answer
Sep 18, 2016

Answer:

#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