U2D19 Notes Name: ___________________________Date: _____________

Solving Absolute Value Equations

1. Explain why the problem |x| = -3 does not have a solution.

2. Explain why the problem |x| = 12 has two different solutions.

3. Solve the equations below:

(a)|x| = 8 (b) |x – 4| = 6

(c) |x – 4| = 0 (d) |2x – 1|= 5

4. What is the sum of and ?

5. Look at the example correctly solved for you below.

|2x + 10| = 4

2x + 10 = 4 2x + 10 = -42x = -6 2x = -14

x = -3 x = -7

6. What values for x will make the following true?|5x – 3 + 2x| = 18

You know that the absolute value of a number must be positive. How is it possible that the value for x can be negative? Prove that the answer given for x is correct by substituting your answers back into the equation and showing you get a true statement.

U2D19 Notes Name: ___________________________Date: _____________

7. You are folding origami cranes that will be used as decorations at a wedding. If you make cranes for 1 hour without a break, you can make 40 cranes. During a 3 hour period you make 100 cranes. How much time did you spend not making cranes?

8. Find the value of x:

9. Solve: |¾ x + 6| = 30

Too much grit to quit!

10. Solve the following absolute value challenge problems. As you find values for x think about what your answer means.

(a) 43 xx (b) xx 5

(c) 77 xx (d) 33 xx