Hi, there:

PROBLEM:
Solve: |2x-5|+24=100

A SOLUTION:
We need to solve this equation for two case: sIn the first, |2x-5| = 2x-5, and in the second, |2x-5| = -(2x-5). 

Case I:
|2x-5| + 24 = 100

Clear the absolute value signs. 2x-5 is positive.
2x - 5 + 24 = 100

Solve for x by combining like terms and isolating x on the left side of the equation.
2x + 19 = 100
2x = 81
x = 40.5

Case II:
|2x-5| + 24 = 100

Clear the absolute value signs. 2x-5 is negative.
-(2x-5) + 24 = 100

Clear the parentheses.
-2x + 5 + 24 = 100

Solve for x by combining like terms and isolating the variable o the left side of the equation.
-2x + 29 = 100
-2x = 71
x = -35.5

Therefore, x=40.5 OR x=-35.5

I always check my work when solving absolute value problems. It's easy to make a 
calculation error.

x = 40.5

|2x-5| + 24 = 100
|2(40.5)-5| + 24 = 100
|81-5| + 24 = 100
|76| + 24 = 100
76 + 24 = 100
100 = 100 check!

OR, x= -35.5

|2x-5| + 24 = 100
|2(-35.5)-5| + 24 = 100
|(-71)-5| + 24 = 100
|-76| + 24 = 100
76 + 24 = 100
100 = 100 check!

That's it! 

Ms. Figgy
math.in.the.vortex@gmail.com