How to Solve Absolute Value Equations
In this article, we shall discuss about solve absolute value equations problems to the students with the help of
online tutor. The equation |x| = 4. How to Solve Absolute Value Equations This means that x could be 4 or x
could be -4. When you take the absolute value of 4, the solution is 4 and when you take the absolute value of
-4, the solution is also 4. An absolute value problem, you have to get into account that there can be two
solutions that will make the equation true. Learning absolute value equation; you set the quantity inside the
absolute value symbol equal to the positive and negative value on the other side of the equal symbol.
Solve absolute value equations
Below are the examples on how to solve absolute value equations -
Example 1: Solve Absolute Value Equations
|x + 1| = 4
Solution:
The quantity inside the absolute value symbol can be equal to 4 or -4
x + 1 = 4 or x + 1 = - 4
Subtract 1 on both side of the given equation
x + 1 - 1 = 4 - 1 or x + 1 - 1 = -4 - 1
x = 3 or x = -5
So the solution are x = 3 and x = -5
Example 2:
|2x - 3| = x - 5
Solution:
When solving this equation, you have to be careful when solving opposite of (x - 5)

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2x - 3 = x - 5 or 2x - 3 = -(x - 5)
x - 3 = -5 or 2x -3 = -x + 5
x = -2 or 3x - 3 = 5
3x = 8
x = [8/3]
So, the solution is x = -2 and x = 8/3 Solve Absolute Value Equations
Example 3:
|x + 1| = 5
Solution:
The quantity inside the absolute value symbol can be equal to 5 or -5
x + 1 = 5 or x + 1 = -5
Subtract 1 on both side of the given equation
x + 1 - 1 = 5 - 1 or x + 1 - 1 = - 5 - 1
x = 4 or x = - 6
So the solution are x = 4 and x = - 6
Practice problems:
Problem 1: |x + 1| = 6
Problem 2: |x + 1| = 7
Solve Absolute Value Equations - answer key:
Problem 1: x = 5 and x = -7
Problem 2: x = 6 and x = -8

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