Lesson 3-4 Solving Multi-Step Inequalities

1. Lesson 3-4Solving Multi-Step Inequalities Objectives: To solve multi-step inequalities with the variable on one and/or both sides.

2. Real-World Connection • Have you ever made or needed a banner? Are you into carpentry? Solving multi-step equations can help you determine the measurements needed for making and building things.

3. STEPS • Simplify. (Get rid of parentheses, fractions, or decimals, combine like terms, etc.) • Undo addition or subtractions. • Undo multiplication or division. Note: Don’t forget to reverse the symbol if mult/div by a negative. • Check.

4. a) -3x - 4 < 14 b) 5 < 7 – 2t Example 1, page 153 Solution: x > -6 • Solution: t < 1

5. c) -8 < 5n - 23 d) 5k + 12 < 2 Example 1 continued Solution: n > 3 Solution: k < -2

6. Example 2, page 154 • To make a second banner, the committee decided to make the length 12 feet. They have 40 feet of a second type of trim. Write and solve an inequality to find the possible widths of the second banner. Solution: w < 8

7. a) 4p+2(p + 7)< 9 b) 15< 5-2(4m+7) Example 3, page 153 Solution: m < -3 Solution: p < -1

8. Example 3, continued • c) 8 > 3(5 - b) + 2 Solution: b > 3

9. Ex. 4) 3b+12 > 27–2b Ex. 5) -6(x-4)>7(2x-3) Examples 4 & 5, page 155 Solution: x < 2.25 Solution: b > 3

10. Summary • What did you learn today?

11. SUMMARY • Solve multi-step inequalities just as you would solve multi-step equations. • Simplify. • Undo add/subt. • Undo mult/div. (Reverse symbol, if needed.) • Check.

12. ASSIGNMENT • #3-4, page 155, Odd 1 – 79, odd 87-103