1-4 Solving Absolute Value Equations Objectives Students will be able to: 1)Evaluate expressions involving absolute values 2)Solve absolute value equations

The absolute value of a number is its distance from 0 on a number line. Distance cannot be negative! Can you walk a negative 3 miles? Think about Ferris Bueller’s Day Off

When evaluating expressions that contain absolute value symbols, the absolute value symbols act as grouping symbols. Always perform any operations inside the absolute value symbols first.

Example 1) Evaluate the expression for y = -3

You try. Example 2)

Absolute Value Equations When solving an absolute value equation there are two cases to examine: IMPORTANT! Before you can remove the absolute value symbol, you have to manipulate the equation so that what is inside the absolute value symbol is on one side of the equal sign, and all other terms are on the other side of the equal sign.

Example 3 Solve each absolute value equation. Check your solutions.

YOU MUST CHECK YOUR WORK!!! There will be instances in which one or both of your solutions do not work!

Try this.

Remember, before you can drop your absolute value symbol, you must get the absolute value term on one side of the equation, and all other terms on the other side. Wait a second, I thought we said back on slide 2 that absolute value can never be negative?????

Because the absolute value of a number is always positive or zero, an equation like is never true. Thus, it has no solution. The solution set for this type of equation is the empty set, symbolized by:

Let’s try some more problems.