Warm Up

1. Week 4 Warm Up 11.10.11 Q N Is ∆NQM ≅ ∆PMQ? Give congruency statements to prove it. M P

2. Absolute value equations have 2 answers. Rule 1 x = 5 5 -5 x = -5 x | | = 5 Ex 1 | 5 | = 5 | -5 | = 5 5 = 5 5 = 5 x = -5 and 5

3. Ex 2 -3 ≤ x < 7 x is greater than or equal to -3 and less than 7 When arrows point toward each other: Rule 2 AND

4. x < -5 or x ≥ 6 Ex 3 x is less than -5 or greater than or equal to 6 When arrows point away from each other: Rule 3 OR

5. Write two equations, one with a positive and one with a negative answer. Rule 4 | x - 2 | = 5 | x - 2 | = 5 Ex 4 x - 2 = -5 x - 2 = 5 x = 5 + 2 x = -5 + 2 x = x = -3 7 | x - 2 | = 5 | -3 - 2 | = 5 | 7 - 2 | = 5 | - 5 | = 5 | 5 | = 5 5 = 5 5 = 5 x = -3, 7

6. Flip the symbol and change the right side to the opposite for second inequality. Rule 5 Ex 5 | 4x - 8 | ≤ 24 4x - 8 ≤ 24 4x - 8 ≥ -24 4x ≥ -24 + 8 4x ≤ 24 + 8 4x ≤ 32 4x ≥ -16 x ≤ 8 x ≥ -4 -4 ≤ x ≤ 8

7. Ex 6 | -2x + 12 | > 6 -2x + 12 > 6 -2x + 12 < -6 -2x < -6 - 12 -2x > 6 - 12 -2x > -6 -2x < -18 x < 3 x > 9 x < 3 or x > 9

8. Ex 7 | -7x + 21 | < -9 Absolute value problems cannot be equal or unequal to a negative number. Rule 6 no solution

9. ______ _____ equations have 2 answers. Review Do: 1 | 6x - 9 | ≤ 27 Assignment: Textbook Page 259, 43 - 59 odds.

10. Ex 5 | 3x + 6 | = 21 3x + 6 = 21 3x + 6 = -21 3x = -21 - 6 3x = 21 - 6 3x = 15 3x = -27 x = 5 x = -9 x = -9, 5