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

Question

Abigail Allen · Accepted Answer

#t=-10" and " t=-2#

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#

Without taking into account the direction of the number, the absolute value tells us how far the number is from the origin.

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

Additionally, algebraic expressions inside the absolute value bars also follow this, so

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

and

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

6 is added 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#

Therefore, t = -10 and t = -2 are the solutions.

Genesis Allen · Answer

undefined To solve the equation abs(t + 6) = 4, you need to consider both the positive and negative cases for the absolute value expression.

Case 1: t + 6 = 4
Solve for t: t = 4 - 6 = -2

Case 2: -(t + 6) = 4
Solve for t: t + 6 = -4
t = -4 - 6 = -10

So, the solutions are t = -2 and t = -10.