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

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.

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.

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

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

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

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

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

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

Summary What did you learn today?

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.

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