Download presentation

1
**Section 4 Solving Inequalities**

Chapter 1 Section 4 Solving Inequalities

2
**Solving Inequalities State whether each inequality is true or false.**

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

3
**Solving Inequalities Solutions 1. 5 < 12, true 3. 5 12, false**

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

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 < x < 11 12 ≥ 2(3n + 1) + 22 12 ≥ 6n ≥ 6n ≥ 6n -2 ≥ n

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

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

8
**Try These Problems Solve. Graph the solution. 2x < 2(x + 1) + 3**

2x < 2x x < 2x < 5 All Real Numbers 4(x – 3) + 7 ≥ 4x + 1 4x – ≥ 4x x + 12 ≥ 4x ≥ 1 No Solution

9
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? Relate: $ % of sales $5000 > – Define: Let x = sales (in dollars). Write: x > – 0.04x Subtract 2000 from each side. > – x 75,000 Divide each side by 0.04. > – 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? x ≥ 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 < 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 ALGEBRA 2 LESSON 1-4 Graph the solution of 3x + 9 < –3 or –2x + 1 < 5. 3x + 9 < –3 or –2x + 1 < 5 3x < – –2x < 4 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

Similar presentations

OK

WARM UP Solve: 1. 3x – 5 = 24. -2(3x -5) = 2 1. 2x – 3 + 4x = 7 1. 3(2x – 4) = 6.

WARM UP Solve: 1. 3x – 5 = 24. -2(3x -5) = 2 1. 2x – 3 + 4x = 7 1. 3(2x – 4) = 6.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on success and failure in business Vector scan display ppt online Ppt on indian textile industries inc Ppt on preposition in hindi Ppt on corruption in indian politics Ppt on different occupations for kids Raster scan display ppt on tv Free download ppt on revolt of 1857 Ppt on save heritage of india Ppt on holographic technology youtube