Algebra Honors ( Period 5)

Chapter 2-5: Absolute Value Equations

When you plug into an expression with absolute value,

the absolute value signs function as parentheses

in Order of Operations.
So make sure you simplify INSIDE before turning that POSITIVE!

Generally, you solve these the same way you solve regular equations.
Make sure you balance equally on both sides!

Follow the steps of a 2-step equation.
1. Add the opposite (you can subtract as well)
2. Multiply by the reciprocal (you can divide as well)

THE DIFFERENCE?
YOU HAVE 2 POSSIBLE ANSWERS!

EXAMPLE: 2 lxl + 1 = 15
2 lxl  + 1 - 1 = 15 - 1
2 lxl  = 14
1/2 ( 2 lxl  ) = 1/2 (14)
 lxl  = 7
x = {-7, 7}

REMEMBER, IF YOU AFTER YOU GET THE ABSOLUTE VALUE ALONE ON ONE SIDE, YOU FIND THAT THE CONSTANT ON THE OTHER SIDE IS NEGATIVE,  
THE ANSWER IS THE NULL SET!

EXAMPLE: 2 lxl + 16 = 15
2 lxl + 16 - 16 = 15 - 16
2 lxl = -1
1/2 ( 2 lxl ) = 1/2 (-1)
 lxl = -1/2
NOT POSSIBLE! So the answer is the null set ∅

We’ll go over how to create an absolute value equation from a graph and how they’re used in real world problems.

The constant inside the absolute value sign is where the middle of the solution is.

If it’s positive, the center is actually a negative number.

If it’s negative, the center is a positive number.

The solution on the other side of the = sign is the DISTANCE from the center on each side of the center.

EXAMPLE:

lx +1l = 12

The center is -1 and the distance from this center is 12 so one solution is -1 + 12 = 11 and the other solution -1 - 12 = -13.

If there is no constant in the absolute value signs,

the center is 0 and the two solutions will be ± the DISTANCE on the other side of =

EXAMPLE:

lxl = 12

The center is 0 and the distance from this center is 12 so one solution is 0 + 12 = 12 and the other solution 0 - 12 = -12 or we can write x = ±12

THE HARDER SKILL IS LOOKING AT A GRAPH AND DETERMINING THE ABSOLUTE VALUE EQUATION THAT IT CAME FROM.

If you really understand the meaning of the parts of the equation, this skill is not as difficult!

HOW DO YOU KNOW IT’S AN ABSOLUTE VALUE EQUATION?

There will generally be TWO solutions graphed.

HOW DO YOU CREATE THE ABSOLUTE VALUE EQUATION?

1. Set up the absolute value signs.
2. Place x inside the absolute value signs.
3. Determine where the center is between the two solutions, FLIP THE SIGN, and place it inside with x.
4. Count the TOTAL DISTANCE between the two solutions, divide it by 2 and place that on the right side of the =.

        This number should always be positive since absolute value       

        is always positive since it’s a distance concept.