In this video, we will be learning how to solve absolute value equations.
***Remember*** Absolute Value is always Positive! (or zero) Therefore, some equations may have No Solution
First subtract 3 to isolate the quantities in the absolute value brackets
Now remove the absolute value brackets and separate the equation into 2 cases as shown below
Let’s go over absolute value equations.
The absolute value is the distance of a number from .
The absolute value is the positive of that number.
No matter what number we put in the absolute value, the answer is always positive.
Even if it’s zero. Zero is neither positive nor negative.
If , we can have two values for .
We can have or
Based on this concept, take a look at this:
Here, we can have two values of .
This makes two equations.
Because as we know earlier, or
First, let’s solve the left equation.
Let’s go to the other equation.
If we substitute these two values into , we’ll know they are both true.
Let’s do it!
So we already proved that both answers are correct.
Let’s take a look at another example.
Before we get our two equations, we have to get the absolute value by itself.
Now, let’s get rid of by subtracting it on both sides.
From here, we have two equations.
Let’s solve both of the equations individually.
Another keypoint is there are some equations that has no solution.
Here, it’s impossible to get the value of to end up with a negative answer.
Because the absolute value of anything is always positive or zero.
Let’s have one more example.
In order to solve this, we have to have by itself.
Let’s solve now by subtracting on both sides.
Then divide by
Now, let’s get the two equations.
Let’s solve on each equation