1 / 15

# Chapter 1

Chapter 1. Section 4 Solving Inequalities. Solving Inequalities. &lt;. &lt;. –. –. &gt;. &gt;. –. –. 7. 3 x + 3 = 2 x – 3. 1. 5 &lt; 12. 8. 5 x = 9( x – 8) + 12. 2. 5 &lt; –12. 3. 5 12. 4. 5 –12. 5. 5 5. 6. 5 5. ALGEBRA 2 LESSON 1-4.

## Chapter 1

An Image/Link below is provided (as is) to download presentation Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

### Presentation Transcript

1. Chapter 1 Section 4 Solving Inequalities

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

3. Solving Inequalities < < – – > > – – ALGEBRA 2 LESSON 1-4 Solutions 1. 5 < 12, true 3. 5 12, false 5. 5 5, true 7. 3x + 3 = 2x – 3 3x – 2x = –3 – 3x = –6 2. 5 < –12, false 4. 5 –12, false 6. 5 5, true 8. 5x = 9(x – 8) + 12 5x = 9x – 72 + 12–4x = –60x = 15

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

5. Solving Inequalities ALGEBRA 2 LESSON 1-4 Solve –2x < 3(x – 5). Graph the solution. –2x < 3(x – 5) –2x < 3x – 15 Distributive Property –5x < –15 Subtract 3x from both sides. x > 3 Divide each side by –5 and reverse the inequality.

6. Try These Problems Solve each inequality. Graph the solution. • 3x – 6 < 27 • 3x < 33 x < 11 • 12 ≥ 2(3n + 1) + 22 • 12 ≥ 6n + 2 + 2212 ≥ 6n + 24-12 ≥ 6n-2 ≥ n

7. 0 Solve 7x≥ 7(2 + x). Graph the solution. 7x≥ 7(2 + x) 7x≥ 14 + 7x Distributive Property 0 ≥ 14Subtract 7x from both sides. The last inequality is always false, so 7x≥ 7(2 + x) is always false. It has no solution.

8. 0 0 Try These Problems Solve. Graph the solution. • 2x < 2(x + 1) + 3 • 2x < 2x + 2 + 32x < 2x + 5 0 < 5All Real Numbers • 4(x – 3) + 7 ≥ 4x + 1 • 4x – 12 + 7 ≥ 4x + 1 4x + 12 ≥ 4x + 1 12 ≥ 1 No Solution

9. > > > > – – – – Relate: \$2000 + 4% of sales \$5000 Define: Let x = sales (in dollars). Write: 2000 + 0.04x 5000 0.04x 3000 Subtract 2000 from each side. x 75,000 Divide each side by 0.04. Solving Inequalities A real estate agent earns a salary of \$2000 per month plus 4% of the sales. What must the sales be if the salesperson is to have a monthly income of at least \$5000? The sales must be greater than or equal to \$75,000.

10. Try This Problem A salesperson earns a salary of \$700 per month plus 2% of the sales. What must the sales be if the salesperson is to have a monthly income of at least \$1800? 700 + .02x ≥ 1800 .02x ≥ 1100 x ≥ 55000 The sales must be at least \$55,000.

11. Compound Inequalities • Compound Inequality – a pair of inequalities joined by and or or • Ex: -1 < x and x ≤ 3 which can be written as -1 < x ≤ 3 • x < -1 or x ≥ 3 • For and statements the value must satisfy both inequalities • For or statements the value must satisfy one of the inequalities

12. And Inequalities • Graph the solution of 3x – 1 > -28 and 2x + 7 < 19. 3x > -27 and 2x < 12 x > -9 and x < 6 • Graph the solution of -8 < 3x + 1 <19 -9 < 3x < 18 -3 < x < 6

13. Or Inequalities 3x < –12 –2x < 4 ALGEBRA 2 LESSON 1-4 Graph the solution of 3x + 9 < –3 or –2x + 1 < 5. 3x + 9 < –3 or –2x + 1 < 5 x < –4 or x > –2

14. Try These Problems • Graph the solution of 2x > x + 6 and x – 7 < 2 • x > 6 and x < 9 • Graph the solution of x – 1 < 3 or x + 3 > 8 • x < 4 or x > 11

15. Homework • Practice 1.4 All omit 23

More Related