Holt Algebra Solving Inequalities with Variables on Both Sides Solve inequalities that contain variable terms on both sides. Objective

Holt Algebra Solving Inequalities with Variables on Both Sides Example 1A: Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. y ≤ 4y + 18

Holt Algebra Solving Inequalities with Variables on Both Sides 4m – 3 < 2m + 6 Example 1B: Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions.

Holt Algebra Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. Check It Out! Example 1a 4x ≥ 7x + 6

Holt Algebra Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. Check It Out! Example 1b 5t + 1 < –2t – 6

Holt Algebra Solving Inequalities with Variables on Both Sides Example 2: Business Application The Home Cleaning Company charges $312 to power-wash the siding of a house plus $12 for each window. Power Clean charges $36 per window, and the price includes power-washing the siding. How many windows must a house have to make the total cost from The Home Cleaning Company less expensive than Power Clean? Let w be the number of windows.

Holt Algebra Solving Inequalities with Variables on Both Sides Example 2 Continued w < 36 w Home Cleaning Company siding charge plus $12 per window # of windows is less than Power Clean cost per window # of windows. times

Holt Algebra Solving Inequalities with Variables on Both Sides Example 3A: Simplify Each Side Before Solving Solve the inequality and graph the solutions. 2(k – 3) > 6 + 3k – 3

Holt Algebra Solving Inequalities with Variables on Both Sides Example 3B: Simplify Each Side Before Solving Solve the inequality and graph the solution. 0.9y ≥ 0.4y – 0.5

Holt Algebra Solving Inequalities with Variables on Both Sides Check It Out! Example 3a Solve the inequality and graph the solutions. 5(2 – r) ≥ 3(r – 2)

Holt Algebra Solving Inequalities with Variables on Both Sides Check It Out! Example 3b Solve the inequality and graph the solutions. 0.5x – x < 0.3x + 6

Holt Algebra Solving Inequalities with Variables on Both Sides There are special cases of inequalities called identities and contradictions.

Holt Algebra Solving Inequalities with Variables on Both Sides

Holt Algebra Solving Inequalities with Variables on Both Sides Example 4A: Identities and Contradictions Solve the inequality. 2x – 7 ≤ 5 + 2x –2x –7 ≤ 5 Subtract 2x from both sides. True statement. The inequality 2x − 7 ≤ 5 + 2x is an identity. All values of x make the inequality true. Therefore, all real numbers are solutions.

Holt Algebra Solving Inequalities with Variables on Both Sides 2(3y – 2) – 4 ≥ 3(2y + 7) 2(3y) – 2(2) – 4 ≥ 3(2y) + 3(7) 6y – 4 – 4 ≥ 6y y – 8 ≥ 6y + 21 Distribute 2 on the left side and 3 on the right side. Example 4B: Identities and Contradictions Solve the inequality. –6y –8 ≥ 21 Subtract 6y from both sides. False statement.  No values of y make the inequality true. There are no solutions.

Holt Algebra Solving Inequalities with Variables on Both Sides 4(y – 1) ≥ 4y + 2 Check It Out! Example 4a Solve the inequality.

Holt Algebra Solving Inequalities with Variables on Both Sides Solve the inequality. x – 2 < x + 1 Check It Out! Example 4b

Holt Algebra Solving Inequalities with Variables on Both Sides Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. t < 5t x – 9 ≤ 4.1x – b + 4(1 – b) > b – 9

Holt Algebra Solving Inequalities with Variables on Both Sides Lesson Quiz: Part II Solve each inequality. 4. 2y – 2 ≥ 2(y + 7) 5. 2(–6r – 5) < –3(4r + 2)