1. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides Students will be able to: Solve inequalities that contain variable terms on both sides. Learning Target

2. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. y ≤ 4y + 18 –10 –8 –6–4 –2 0246810 4m – 3 < 2m + 6 4 5 6

3. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. 4x ≥ 7x + 6 –10 –8 –6–4 –2 0246810

4. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides 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? 13 < w The Home Cleaning Company is less expensive for houses with more than 13 windows.

5. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. 2(k – 3) > 6 + 3k – 3 –12–9–6–303

6. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solution. 0.9y ≥ 0.4y – 0.5 –5 –4 –3–2 –1 01234 5

7. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. 0.5x – 0.3 + 1.9x < 0.3x + 6 –5 –4 –3–2 –1 01234 5

8. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides There are special cases of inequalities called identities and contradictions.

9. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides

10. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides Solve the inequality. 2x – 7 ≤ 5 + 2x The inequality 2x − 7 ≤ 5 + 2x is an identity. All values of x make the inequality true. Therefore, all real numbers are solutions.

11. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides 2(3y – 2) – 4 ≥ 3(2y + 7) Solve the inequality. No values of y make the inequality true. There are no solutions. HW pp.197-199/20-38,40-48even,49-51,56-66,73-76

12. Holt Algebra 1 3-5 Solving Inequalities with Variables on Both Sides Warm Up Solve each equation. 1. 2x = 7x + 15 2. 5. Solve and graph 5(2 – b) > 5 2. 3. 2(3z + 1) = – 2(z + 3) 4. 3(p – 1) = 3p + 2 x = –3 b < –3 –5 –3–2–1 –4 0 –6 3y – 21 = 4 – 2yy = 5 z = –1 no solution