Friday, January 27, 2023

### What is the Solution to |x| - |x-2| = 2?

Solving equations with absolute values can be tricky. In this article, we will discuss the solution to the equation |x| - |x-2| = 2. We will look at the steps to solve this equation and provide examples to help you understand the process.

• Understand the absolute value of a number

• Consider two cases: when x is positive and when x is negative

• Solution to the equation |x| - |x-2| = 2 is x = 4 when x is positive and x = -6 when x is negative

The equation |x| - |x-2| = 2 can be solved by first understanding the absolute value of a number. The absolute value of a number is the distance of the number from 0 on the number line. For example, the absolute value of -3 is 3, and the absolute value of 3 is also 3. This means that the absolute value of a number is always positive.

Now that we understand the absolute value of a number, we can solve the equation |x| - |x-2| = 2. To solve this equation, we must first determine the value of x. To do this, we must consider two cases: when x is positive and when x is negative. If x is positive, then the equation becomes x - (x-2) = 2. Solving this equation gives us x = 4. If x is negative, then the equation becomes -x - (-x-2) = 2. Solving this equation gives us x = -6.

To summarize, the solution to the equation |x| - |x-2| = 2 is x = 4 when x is positive and x = -6 when x is negative.

Good to know:

• Absolute Value: The distance of a number from 0 on the number line

In conclusion, the solution to the equation |x| - |x-2| = 2 is x = 4 when x is positive and x = -6 when x is negative. Understanding the absolute value of a number is key to solving equations with absolute values.