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.
The information provided in this article is for educational purposes only and should not be used as a substitute for professional advice.
