1. Chapter 6.4

2.  Reminder: What are we trying to do when we solve an inequality?  Answer:  To get the variable by itself

3.  Example 1:  First we must get the term with the x by itself.  Subtract 3 from both sides  Divide both sides by 2 2x+ 3<9 - 3 6 2 x3

4. 1. 3x + 5 > 14 2. 6x + 2 ≤ 20 3. 23 ≥ 2x + 7 4. 8 + 3x > 32 5. - 9 < 3 + 4x

5.  Example 2: ≤  Add 5 to both sides  Divide both sides by 3 3x- 57 +5 12 3 x 4

6. 1. 2x – 5 > 7 2. 4x – 3 ≥ -15 3. 6 ≤ 5x – 9 4. -7 < 2x – 7

7.  Example 3:  Subtract 3 from both sides  Divide both sides by -2  Remember, when you divide both sides by a negative you have to switch the sign -2x+ 3 > 9 -3 6 -2 x-3

8. 1. -3x + 5 ≤ 17 2. -5x – 7 > 8 3. 7 – 4x ≥ 3 4. -8 ≤ 6 – 7x

9.  Example 4:  Rewrite with the x on the top of the fraction  Multiply both sides by 3  Divide both sides by 2  Simplify x>43(3)2x 12 2 x 6

10. 1. x > 9 2. x ≤ -6 3. -10 < - x 4. - ≥ 4 3232 3434 5252 6767

11.  Example 5:  To get the x by itself we have to get rid of the fraction first  Multiply both sides by 5  Subtract 3 from both sides  Divide by 2 ≥7 5 (5)2x + 335 -3 2x 32 2 x 16

12. 1. ≥ 5 2. ≤ -6 3. -4 > - 4. < 7 2x + 3 7 4x + 4 3 3x + 5 5 5 - 2x 3

13. 1. 4x + 7 > - 5 2. 9 ≤ 7 – 6x 3. -3x – 10 ≥ - 16 4. x ≤ -6 5. < 7 3434 2x + 5 3