SOLUTION: Solve the following problem: |2x-7|-5=4

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|2x-7|-5=4

Add 5 both sides
|2x - 7| = 9

This Equation is equivalent to a combined equation containing or , a disjunction. THe equation has two solutions.
2x - 7 = 9 or 2x - 7 = -9

Solve for x:
1. 2x - 7 = 9
2x = 16
x = 8


2. 2x - 7 = -9
2x = -2
x = -1


Checking
|2x - 7| - 5 = 4

When x = 8
|2(8) - 7| - 5 = 4
|9| - 5 = 4
9 - 5 = 4
4 = 4 ---> true


when x = -1
|2x -7| - 5 = 4
|2(-1)- 7| - 5 = 4
|-2 - 9| - 5 = 4
|-9| - 5 = 4
9 - 5 = 4
4 = 4 ---> True

It is important to check your solution in the original equation.

Since both values makes the |2x-7|-5 = 4 true, therefore, the solution set is {8, -1}