Absolute Value Solution Sets

Before we start with this lesson I would like to explain this symbol |x| you read it as the absolute value of x. This means the absolute value of the number’s distance to 0 on the number line. The absolute value of a number will always be positive. For example |-4| = 4 and |4| = 4, now that we have finished talking about the absolute value let’s focus on the main topic.

Here we are given a problem which is y = | 2x – 5 | = 4, we know that we have to solve for x, and x could either be – or +, let’s first use +4 for the equation, as you can see from the image below we have got the answer 4.5. Now let’s use -4, and we got the answer 0.5 so x is with 4.5 or 0.5.