How do you solve #abs(2x-3)=5#?

2 Answers
Jun 19, 2018

#x=-1#

#x=4#

Explanation:

As explained below:

Step 1: Clear the absolute value bars

#|2x-3|=5#

For negative part, lets use #-(2x-3)#

For positive part, lets use #(2x-3)#

Step 2: Solve the negative part

#-(2x-3) = 5#

#-2x+3 = 5#

#-2x=5-3#

#-2x=2#

#x=-2/2 = -1#

#x=-1# ----> solution for the negative part

Step 3: Solve the positive part

#(2x-3)=5#

#2x=5+3#

#2x=8#

#x=8/2#

#x=4# ------> solution for the positive part

So values of x are #x=-1# and #x=4#

Jun 19, 2018

#x=-1" or "x=4#

Explanation:

#"the expression inside the absolute value can be positive"#
#"or negative"#

#color(magenta)"positive expression"#

#2x-3=5rArr2x=5+3=8rArrx=4#

#color(magenta)"negative expression"#

#-(2x-3)=5#

#-2x+3=5#

#-2x=5-3=2#

#x=2/(-2)=-1#

#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.

#x=-1#

#|-2-3|=|-5|=5#

#x=4#

#|8-3|=|5|=5#

#x=-1" or "x=4" are the solutions"#