# How do you solve #|1/2t - 3| = 1#?

##### 1 Answer

May 13, 2018

#### Explanation:

#"the expression inside the absolute value bars can be "#

#"positive or negative hence there are 2 possible solutions"#

#color(magenta)"positive expression"#

#1/2t-3=1#

#"add 3 to both sides and multiply by 2"#

#rArr1/2t=1+3=4#

#rArrt=2xx4=8#

#color(magenta)"negative expression"#

#-1/2t+3=1#

#"subtract 3 from both sides and multiply by "-2#

#rArr-1/2t=1-3=-2#

#rArrt=-2xx-2=4#

#color(blue)"As a check"# Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

#t=4rArr|2-3|=|-1|=1#

#t=8rArr|4-3|=|1|=1#

#rArrt=4" or "t=8" are the solutions"#