Absolute Value Equation

Need to know how to solve an absolute value equation like this one?

|x - 4| = 6

Don't be intimidated: Remember, the definition of absolute value is the distance a number is from zero. All this really means is the number must be positive, because a distance has to be positive! Quite simply, you must account for when the value is positive, and when it is negative - there are two separate answers

Let's solve the problem below together!

|2x + 5| − 3 = 8

Step 1: Isolate the absolute value

New equation - |2x + 5| = 11 (add 3 to each side)

 

Step 2: Make two equations, One positive & One negative

Step 3: Solve each equation

Notice above, the two answers are x = 3 and x = −8.

If you are curious as to why I changed the sign of the number on the right instead of the quantity on the left, it was simply to make things easier. In effect, it is the same as dividing both sides by −1.

For an additional challenge, try solving absolute value inequalities. Otherwise, take another look at an absolute value equation.