Warm Up 8r + 4 = 10 + 2r 28 – 0.3y = 0.7y – 12 8x + 6 – 9x = 2 – x – 15 Jon and Sara are planting tulip bulbs. Jon has planted 60 bulbs and is planting at a rate of 44 bulbs per hour. Sarah has planted 96 bulbs and is planting at a rate of 32 bulbs per hour. In how many hours will Jon and Sara have planted the same number of bulbs? How many bulbs will that be?

Solving Absolute Value Equations

In a game show, a contestant guesses the price of an item and wins a prize if his or her guess does not differ from the actual price by more than $5. The actual price is $48. What guesses will win a prize?

Would a contestant guessing $50 be any more correct that a contestant guessing $46?

What is absolute value? Absolute value represents a distance from 0. Because distance can be in the positive or negative direction from 0, there can be as many as two possible answers for an absolute-value equation.

The equation above asks, what values of x have an absolute value of 5?

The solutions are 5 and -5.

The equation above asks, what values of x have an absolute value of a?

The solutions are “a” and the “opposite of a”.

Absolute value can never be 0 Absolute value can never be 0. Therefore, there is no solution to the equation or any absolute value equation that equals a negative number.

Most absolute value equations will have two solutions. Think about the equation: What can x + 4 equal? (It can equal 13 or -13)

Most absolute value equations will have two solutions. Therefore, we must set up two cases and solve each case to get two solutions.

Case 1 Case 2 X + 4 = 13 x + 4 = - 13

Steps to Solving Absolute Value Equations Isolate the absolute value expression. (Using Inverse Operations) Rewrite the equation as two cases. Solve for the variable in both equations.

Solution Sets { } Solution sets are efficient when an equation has more than one solution. The solution set should be written with both solutions inside of the { }

Example 1.

Example 2.

Example 3.

Example 4.

{-58, 58}

Example 5.

{0, 4}

Example 6.

No Solution

Example 7.

{4}

Create your own absolute Value Equation on your paper and pass it to your neighbor to solve.