1. 2-step inequalities  Earlier in the year, we learned how to solve inequalities. Remember what the open circle And closed circle represent?

2. 2-step inequalities  Earlier in the year, we learned how to solve inequalities. Remember what the open circle And closed circle represent? Open circle represents and Closed circle represents

3. 2-step inequalities  We also learned that if an inequality was greater than we highlighted the right (or greater) side of the number line:  If the inequality was less than we highlighted the left (or less) side of the number line:

4. 2-step inequalities  When we solve 2-step inequalities, we solve just as if the problem had an equals sign.  For example consider the problem: 2y – 3 < -5

5. Example  2y – 3 < -5 +3 +3add 3 to both sides 2y < -2 2 2divide both sides by 2 y < -1 graph -3 -2 -1 0 1 2 3

6. Another example  Don’t forget: if you multiply or divide by a negative number, you must reverse the inequality sign.  -9 > x + 6 -3 -9 > x + 6 -6 -3 -6subtract 6 (-3)-15 > x (-3) -3multiply by -3 45 45

7. Try These: 1. 5a – 9 > 11 2. 17 +.5 c <14 3. 6 – x > 3 4. 8.3 < -0.5b – 2.7 5. 4x + 5 ≥ 21 6. -14≤ -2p + 7 7. 11 + 8c ≥ 9c

8. Answers: 1. 5a – 9 > 11a > 4 2. 17 +.5 c <14c < -6 3. 6 – x > 3x < 3 4. 8.3 < -0.5b – 2.7b < -22 5. 4x + 5 ≥ 21x ≥ 4 6. -14≤ -2p + 7p ≤ 10.5 7. 11 + 8c ≥ 9cc ≤ 11

9. 2-Step Inequalities Worksheet:  Complete the two – step inequalities worksheet.  Show all work and graph your answers on the given number lines.  REMEMBER: Open versus Closed Circles!