Absolute Value Equation
An absolute value equation is an equation that contains an absolute value expression
An absolute value equation is an equation that contains an absolute value expression. An absolute value expression is written as |x|, where “x” can be any real number. The purpose of absolute value is to compute the distance of a number from zero on a number line, making it always positive.
The general form of an absolute value equation is: |expression| = constant
To solve an absolute value equation, you need to isolate the absolute value expression and consider two cases, one for when the expression inside the absolute value is positive or zero, and another one for when it is negative.
Let’s work through an example to illustrate the process of solving an absolute value equation:
Example: Solve the equation |3x – 2| = 5
Step 1: Set up two cases:
Case 1: 3x – 2 > 0
Case 2: 3x – 2 < 0
Step 2: Solve each case separately:
Case 1: 3x - 2 > 0
Add 2 to both sides:
3x – 2 + 2 > 0 + 2
3x > 2
Divide by 3:
x > 2/3
Case 2: 3x – 2 < 0 Add 2 to both sides: 3x - 2 + 2 < 0 + 2 3x < 2 Divide by 3: x < 2/3 Step 3: Combine the solutions from both cases: The solution is x < 2/3 or x > 2/3.
This means that x can be any real number less than 2/3 or any real number greater than 2/3 that satisfies the original equation.
It is important to check the solution by substituting the values back into the original equation to ensure they are valid solutions.
I hope this explanation helps you understand how to solve absolute value equations. If you have any further questions, feel free to ask!
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