Section 5 Solving Inequalities Chapter 1 Section 5 Solving Inequalities

Solving Inequalities State whether each inequality is true or false. ALGEBRA 2 LESSON 1-4 State whether each inequality is true or false. 1. 5 < 12 2. 5 < –12 3. 5 12 4. 5 –12 > – < – 5. 5 5 6. 5 5 < – > – Solve each equation. 7. 3x + 3 = 2x – 3 8. 5x = 9(x – 8) + 12

Inequalities The solutions include more than one number Ex: 2 < x ;values that x could be include 3, 7, 45…

Inequalities All of the rules for solving equations apply to inequalities, with one added: If you multiply or divide by a NEGATIVE you must FLIP the sign. (< becomes > and > becomes <)

Inequalities When graphing on a number line: Open dot for < or > Closed (solid) dot for ≤ or ≥ The shading should be easy to see (a slightly elevated line is ok) --- see examples

Solving Inequalities Solve –2x < 3(x – 5). Graph the solution. ALGEBRA 2 LESSON 1-4 Solve –2x < 3(x – 5). Graph the solution.

Try These Problems Solve each inequality. Graph the solution. 3x – 6 < 27 3x < 33 x < 11 12 ≥ 2(3n + 1) + 22 12 ≥ 6n + 2 + 22 12 ≥ 6n + 24 -12 ≥ 6n -2 ≥ n

Solve 7x ≥ 7(2 + x). Graph the solution.

Try These Problems Solve. Graph the solution. 2x < 2(x + 1) + 3 2x < 2x + 2 + 3 2x < 2x + 5 0 < 5 All Real Numbers 4(x – 3) + 7 ≥ 4x + 1 4x – 12 + 7 ≥ 4x + 1 4x - 5 ≥ 4x + 1 -5 ≥ 1 No Solution

Assignment: Skills Practice WS