Warm Up - PowerPoint PPT Presentation

• 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?

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.

Absolute value can never be 0. Therefore, there is no solution to the equation or

any absolute value equation that equals a negative number.

Think about the equation:

What can x + 4 equal?

(It can equal 13 or -13)

Therefore, we must set up two cases and solve each case to get two solutions.

X + 4 = 13 x + 4 = - 13

• Isolate the absolute value expression. (Using Inverse Operations)
• Rewrite the equation as two cases.
• Solve for the variable in both equations.

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

{-58, 58}

{0, 4}

No Solution

{4}