1 / 19

Solve inequalities that contain variable terms on both sides.

Learn to solve inequalities with variable terms on both sides & graph solutions like a pro. Practice business applications & simplify sides before solving. Identify identities & contradictions. Quiz included.

kbrandon
Download Presentation

Solve inequalities that contain variable terms on both sides.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Objective Solve inequalities that contain variable terms on both sides.

  2. Example 1A: Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. y ≤ 4y + 18

  3. Example 1B: Solving Inequalities with Variables on Both Sides Solve the inequality and graph the solutions. 4m – 3 < 2m + 6

  4. Check It Out! Example 1a Solve the inequality and graph the solutions. 4x ≥ 7x + 6

  5. Check It Out! Example 1b Solve the inequality and graph the solutions. 5t + 1 < –2t – 6

  6. Example 2: Business Application 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? Let w be the number of windows.

  7. Home Cleaning Company siding charge Power Clean cost per window is less than # of windows. # of windows times $12 per window plus times Example 2 Continued 312 + 12 • w < 36 • w

  8. Example 3A: Simplify Each Side Before Solving Solve the inequality and graph the solutions. 2(k – 3) > 6 + 3k – 3

  9. Example 3B: Simplify Each Side Before Solving Solve the inequality and graph the solution. 0.9y ≥ 0.4y – 0.5

  10. Check It Out! Example 3a Solve the inequality and graph the solutions. 5(2 – r) ≥ 3(r – 2)

  11. Check It Out! Example 3b Solve the inequality and graph the solutions. 0.5x – 0.3 + 1.9x < 0.3x + 6

  12. There are special cases of inequalities called identities and contradictions.

  13. –2x –2x Example 4A: Identities and Contradictions Solve the inequality. 2x – 7 ≤ 5 + 2x 2x – 7 ≤ 5 + 2x Subtract 2x from both sides.  –7 ≤ 5 True statement. The inequality 2x − 7 ≤ 5 + 2x is an identity. All values of x make the inequality true. Therefore, all real numbers are solutions.

  14. –6y –6y Example 4B: Identities and Contradictions Solve the inequality. 2(3y – 2) – 4 ≥ 3(2y + 7) Distribute 2 on the left side and 3 on the right side. 2(3y – 2) – 4 ≥ 3(2y + 7) 2(3y) – 2(2) – 4 ≥ 3(2y) + 3(7) 6y – 4 – 4 ≥ 6y + 21 6y – 8 ≥ 6y + 21 Subtract 6y from both sides.  –8 ≥ 21 False statement. No values of y make the inequality true. There are no solutions.

  15. Check It Out! Example 4a Solve the inequality. 4(y – 1) ≥ 4y + 2

  16. Check It Out! Example 4b Solve the inequality. x – 2 < x + 1

  17. Lesson Quiz: Part I Solve each inequality and graph the solutions. 1. t < 5t + 24 2. 5x – 9 ≤ 4.1x –81 3. 4b + 4(1 – b) > b – 9

  18. Lesson Quiz: Part II Solve each inequality. 4. 2y – 2 ≥ 2(y + 7) 5. 2(–6r – 5) < –3(4r + 2)

More Related