1. ALGEBRA 1 Lesson 3-4 Warm-Up

2. ALGEBRA 1 Lesson 3-4 Warm-Up

3. ALGEBRA 1 “Solving Multi-Step Inequalities” (3-4) (3-1) How do you solve a multi-step inequality? Tip: Solve a multi-step inequality exactly like an equality (equation with an equal sign). Isolate the variable (get the letter by itself) by: 1. “Undo”ing addition and subtraction from the variable side 2. “Undo”ing multiplication and division from the variable side Note: If the variables is on both sides, “undo” it from one side so that there is only one variable side before doing anything else

4. ALGEBRA 1 Example: Solve 2y – 3  -5. 2y - 3 + 3  -5 + 3Add 3 to each side. 2y + 0  -2 Simplify. y  -1Simplify. Check: 2y - 3  -5 2y - 3  -5Check the direction of the inequality. 2(-2) - 3  -5Substitute a solution less than – 1 for b like -2. 2(-1) - 3 -5Substitute -1 for y. -5 = -5 -7  -5 The direction of the sign is correct.  Divide each side by 2. 2y 2 -2 2 “Solving Two-Step Inequalities” (7-5) (3-1)

5. ALGEBRA 1 Example: Solve -9 – x + 6.  1313 -9 – x + 6  1313 -9 - 6 – x + 6 - 6  1313 Add 6 to each side. Simplify. -15 – x + 0  1313 Simplify. 45  x or x  45 3131 –(-15) 3131 – 1313 –x To eliminate the coefficient - from the x side, divide both sides by - which is the same as multiplying each side by the reciprocal, - When you divide or multiply both sides by a negative, reverse the direction of the inequality symbol. 1313  1313 3131 Check: -9  – x + 6 1313 -9  – (45) + 6 Substitute 45 for x. 1313 -9 = -9 -9  – (60) + 6 Check the direction of the inequality by substituting x for a value bigger than 45, like 60. 1313 -9  -14 The direction of the sign is correct. “Solving Multi-Step Inequalities” (3-4) -1)

6. ALGEBRA 1 Solve 6 – r – 6. < 2323 6 – r – 6 < 2323 6 + 6 – r – 6 + 6 < 2323 Add 6 to each side. Simplify. 12 – r < 2323 Simplify. > –18 r, or r –18 < 3232 –(12) 3232 – 2323 –r Multiply each side by. Reverse the direction of the inequality symbol. 3232 – > Solving Two-Step Inequalities LESSON 7-5 Additional Examples

7. ALGEBRA 1 Solve 5 + 4b < 21. 5 + 4b – 5 < 21 – 5Subtract 5 from each side. 4b < 16Simplify. b < 4Simplify. Check: 5 + 4b = 21Check the computation. 5 + 4b < 21Check the direction of the inequality. 5 + 4(3) < 21Substitute 3 for b. 5 + 4(4) 21Substitute 4 for b. 21 = 21 17 < 21 < Divide each side by 4. 4b44b4 16 4 Solving Multi-Step Inequalities LESSON 3-4 Additional Examples

8. ALGEBRA 1 The band is making a rectangular banner that is 20 feet long with trim around the edges. What are the possible widths the banner can be if there is no more than 48 feet of trim? twice the the length length of the trim Words:plus twice the width can be no more than Equation:2(20) + 2w 48 < Solving Multi-Step Inequalities LESSON 3-4 Additional Examples

9. ALGEBRA 1 (continued) The banner’s width must be 4 feet or less. 2(20) + 2w 48 < 40 + 2w 48Simplify 2(20). < 40 + 2w – 40 48 – 40Subtract 40 from each side. < 2w 8Simplify. < w 4Simplify. < Divide each side by 2. < 2w22w2 8282 Solving Multi-Step Inequalities LESSON 3-4 Additional Examples

10. ALGEBRA 1 Solve 3x + 4(6 – x) < 2. 3x + 24 – 4x < 2Use the Distributive Property. –x + 24 < 2Combine like terms. –x + 24 – 24 < 2 – 24Subtract 24 from each side. –x < –22Simplify. x > 22Simplify. > Divide each side by –1. Reverse the inequality symbol. –x –1 –22 –1 Solving Multi-Step Inequalities LESSON 3-4 Additional Examples

11. ALGEBRA 1 a.) Solve 8z – 6 < 3z + 12. 8z – 6 – 3z < 3z + 12 – 3z“Undo” the variable from one side first by subtracting 3z from each side. 5z – 6 < 12Combine like terms. 5z – 6 + 6 < 12 + 6Add 6 to each side. 5z < 18Simplify. < Divide each side by 5. 5z55z5 18 5 z < 3Simplify. 3535 Solving Multi-Step Inequalities LESSON 3-4 Additional Examples

12. ALGEBRA 1 b.) Solve 5(–3 + d) 3(3d – 2). < –15 – 4d + 15 –6 + 15Add 15 to each side. < –4d 9Simplify. < –15 + 5d – 9d 9d – 6 – 9dSubtract 9d from each side. < –15 – 4d –6Combine like terms. < –15 + 5d 9d – 6Use the Distributive Property. < d –2Simplify. > 1414 Divide each side by –4. Reverse the inequality symbol. –4d –4 9 –4 > Solving Multi-Step Inequalities LESSON 3-4 Additional Examples

13. ALGEBRA 1 Solve each inequality. 1.8 + 5a 232.– p < p – 6 3.3(x – 4) > 4x + 74.3(3c + 2) 2(3c – 2) > < 1313 1212 a 3 > p > 7 1515 x < –19 < c –3 1313 Solving Multi-Step Inequalities LESSON 3-4 Lesson Quiz