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

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

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

Holt Algebra 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.

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

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

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

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 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.

Holt Algebra 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 /20-38,40-48even,49-51,56-66,73-76

Holt Algebra Solving Inequalities with Variables on Both Sides Warm Up Solve each equation. 1. 2x = 7x Solve and graph 5(2 – b) > (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