1. Lesson 6.5 Solve Absolute Value Equations
Essential Question: How do you solve absolute value equations?

2. Before we start…
Why do −8 =8 and 8 =8 have the same solution?

3. What is absolute value?
The distance a number is from zero on the number line.

7. How do you solve absolute value equations?
Given 𝑎𝑥+𝑏 =𝑐
Write two equations
𝑎𝑥+𝑏=𝑐 and 𝑎𝑥+𝑏=−𝑐
Solve each equation.
Check each solution.

14. Can there be no solution?
Yes there can be.
The absolute value of a number is never negative so if the equation equals a negative number, there is no solution.

16. What is absolute deviation?
It is the absolute value of the difference of x and the given value.
The absolute deviation can also be known as the absolute error if it’s a measured value from an accepted value.

17. Basketballs Before the start of a professional basketball game, a basketball must be inflated to an air pressure of 8 pounds per square inch (psi) with an absolute error of 0.5 psi. Find the minimum and maximum acceptable air pressures for the basketball.

18. Guardrails A safety regulation requires that the height of a guardrail be 42 inches with an absolute deviation of 3 inches. Find the minimum and maximum heights of a guardrail.

19. Cheerleading A cheerleading team is preparing a dance program for a competition. The program must last 4 minutes with an absolute deviation of 5 seconds. Find the least and greatest possible times (in seconds) that the program can last.

20. Jewelry A jewelry store advertisement states that a certain diamond bracelet weighs 12 carats, but the actual weight can vary by as much as 5% of the advertised weight. Find the minimum and maximum possible weights of the bracelet.

21. How do you solve absolute value equations?

22. Ticket Out the Door