Absolute value is a mathematical function that returns the non-negative value of a number. When it comes to solving equations involving absolute value, things can get a little tricky. But fear not! In this blog post, we will walk you through the steps to easily solve equations with absolute value. So let’s get started.

What is an Absolute Value Equation?

An absolute value equation is an equation that involves the absolute value of a variable. It usually takes the form of |x| = a, where x represents the variable and a is a constant.

How to Solve Absolute Value Equations

Solving absolute value equations involves considering two separate cases:

  • Case 1: When the expression inside the absolute value is positive or zero.
  • Case 2: When the expression inside the absolute value is negative.

Let’s dive deeper into each case.

Case 1: Expression is Positive or Zero

When the expression inside the absolute value is greater than or equal to zero, it means there is no need for change. In this case, the equation |x| = a can be rewritten as:

x = a or x = -a

For example, if you have the equation |2x – 3| = 5, by eliminating the absolute value, you get two simple linear equations: 2x – 3 = 5 and 2x – 3 = -5. Solve each equation separately to find the values of x.

Case 2: Expression is Negative

When the expression inside the absolute value is negative, you must change the sign to make it positive before solving the equation. In this case, the equation |x| = -a can be rewritten as:

x = -a or x = a

For example, if you have the equation |x + 2| = -3, ignore the negative sign and rewrite the equation as x + 2 = 3. Solve for x and check if it satisfies the requirement of the absolute value equation. If not, the equation has no solution.

Final Thoughts

Solving equations with absolute value may appear daunting at first, but with the right approach, it becomes manageable. Remember to consider both cases and analyze the expression inside the absolute value to solve the equation accurately. Keep practicing, and soon you’ll become proficient in solving these types of equations.

We hope this blog post has shed light on how to solve equations with absolute value. If you have any further questions or need clarification, feel free to reach out to us in the comments below. Happy math solving!

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