Solving Inequalities with variables on both sides of the Sign Chapter 6.3

Solving Inequalities with variables on both sides of the Sign Lesson Objective: NCSCOS 4.01- Use linear functions to model and solve problems Students will know how to solve equations with variables on both sides. Students will know how to use the distributive property to solve problems. Students will know how to combine like terms to solve problems

Solving Inequalities with variables on both sides of the Sign 5x 2x - 8 x 10 < 20 3x + 12 Example 1: First we must get all the variables on one side of the equation. Subtract 3x from both sides Second we have to get all the numbers on the other side Add 8 to both sides Divide both sides by 2 -3x -3x 2 2 + 8 +8

Solving Inequalities with variables on both sides of the Sign 6 – x > 5x + 30 5y – 4y ≥ 3y + 2 4m – 8 ≤ 10 – 2m 8 + 4k < -10 + k (2/5)x – 8 ≤ 9 – (3/5)x Practice

Solving Inequalities with variables on both sides of the Sign Example 2: Distribute on both sides Add 10x to both sides Add 4 to both sides Divide by 18 4(2x – 1) ≥ -10(x – 5) 18x – 4 ≥ 50 8x – 4 ≥ -10x + 50 18x ≥ 54 x ≥ 3 +10x +10x +4 +4 18 18

Solving Inequalities with variables on both sides of the Sign -3(x + 5) < 3(x – 1) 5(x + 2) ≤ 2(3 – x) 4(m + 3) > 36 4(y – 2) < 2(5 – y) 3(x – 8) ≥ 3x More Practice

Solving Inequalities with variables on both sides of the Sign Example 3: Distribute on both sides Combine like terms on either side of the equals sign Subtract 3x from both sides Subtract 24 from both sides Divide by 2 5(x + 3) + 9 > 3(x – 4) + 6 5x + 15 + 9 > 3x – 12 + 6 5x + 24 > 3x - 6 2x + 24 > -6 __ 2x > -30 x > -15 __ -3x -3x -24 -24 2 2

Solving Inequalities with variables on both sides of the Sign 3(x – 8) – 5 ≤ 9(x + 2) + 1 2(x + 2) + x ≥ 5 + 4(x – 2) 5x – (3x – 3) > 2x + 3(x + 4) Last Practice!

Solving Inequalities with variables on both sides of the Sign Quiz 6.3 2x + 3 ≤ 3x – 5 7x – 3 > 3 – 2x 2(x + 3) ≥ 3(x – 4) 5(2x – 4) < -6(2 – x) 3(x + 2) – 2x > 4(x -3) + 6