1 / 21

Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 7. 13. 1. 8. 16. 16. x = – . Warm Up Solve. 1. 6 x + 36 = 2 x 2. 4 x – 13 = 15 + 5 x 3. 5( x – 3) = 2 x + 3 4. + x = . x = –9. x = –28. x = 6. California Standards.

evania
Download Presentation

Warm Up

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. Preview Warm Up California Standards Lesson Presentation

  2. 7 13 1 8 16 16 x = – Warm Up Solve. 1.6x + 36 = 2x 2. 4x – 13 = 15 + 5x 3. 5(x – 3) = 2x + 3 4. + x = x = –9 x = –28 x = 6

  3. California Standards AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results.

  4. When you solved two-step equations, you used the order of operations in reverse to isolate the variable. You can use the same process when solving two-step inequalities.

  5. 1 2 3 4 5 6 7 12 4x > 4 4 Additional Example 1A: Solving Two-Step Inequalities Solve and graph. 4x + 1 > 13 4x + 1 > 13 – 1– 1Since 1 is added to 4x, subtract 1 from both sides. 4x > 12 Since x is multiplied by 4, divide both sides by 4. x > 3

  6. Additional Example 1A Continued Check According to the graph 4 should be a solution and 2 should not be a solution. x > 3 x > 3 Substitute 4 for x. Substitute 2 for x. ? ? 4 > 3 2 > 3  So 4 is a solution. So 2 is not a solution.

  7. Remember! If both sides of an inequality are multiplied or divided by a negative number, the inequality symbol must be reversed.

  8. -6 -5 -4 -3 -2 -1 0 18 –9x –9 –9 Additional Example 1B: Solving Two-Step Inequalities Solve and graph. –9x + 7  25 –9x + 7  25 – 7– 7Subtract 7 from both sides. –9x 18 Divide each side by –9; change  to . x–2

  9. 1 2 3 4 5 6 7 10 5x > 5 5 Check It Out! Example 1A Solve and graph. 5x + 2 > 12 5x + 2 > 12 – 2– 2Subtract 2 from both sides. 5x > 10 Divide both sides by 5. x > 2

  10. Check It Out! Example 1A Continued Check According to the graph 4 should be a solution and 1 should not be a solution. x > 2 x > 2 Substitute 4 for x. Substitute 1 for x. ? ? 4 > 2 1 > 2  So 4 is a solution. So 1 is not a solution.

  11. -6 -5 -4 -3 -2 -1 0 16 –4x –4 –4 Check It Out! Example 1B –4x + 2  18 –4x + 2  18 – 2– 2Subtract 2 from both sides. –4x 16 Divide each side by –4; change  to . x–4

  12. +  20( + ) 20( ) 2x 2x 2x 2x 3 3 3 3 9 9 9 9 5 5 5 5 4 4 4 4 10 10 10 10 20( ) + 20( ) 20( ) Additional Example 2: Solving Inequalities That Contain Fractions Solve +  and graph the solution. Multiply by LCD, 20. Distributive Property. 8x + 15 18 – 15– 15Since 15 is added to 8x, subtract 15 from both sides. 8x 3

  13. Since x multiplied by 8, divide both sides by 8. x  8x 3 3 8 8 8 0 1 3 8 Additional Example 2 Continued 8x 3

  14. +  Solve +  20( + )20( ) 3x 3x 3x 3x 1 1 1 1 5 5 5 5 5 5 5 5 4 4 4 4 10 10 10 10 20( ) + 20( ) 20 ( ) Check It Out! Example 2 Multiply by LCD, 20. Distributive Property. 12x + 5 10 – 5– 5Since 5 is added to 12x, subtract 5 from both sides. 12x 5

  15. x  Since x is multiplied by 12, divide both sides by 12. 12x 5 5 12 12 12 0 5 12 Check It Out! Example 2Continued 12x 5

  16. Additional Example 3: School Application A school’s Spanish club is selling bumper stickers. They bought 100 bumper stickers for $55, and they have to give the company 15 cents for every sticker sold. If they plan to sell each bumper sticker for $1.25, how many do they have to sell to make a profit? In order for the Spanish club to make a profit, the revenue must be greater than the cost. 1.25x > 55 + 0.15x

  17. 55 > 1.10x 1.10 1.10 Additional Example 3 Continued 1.25x > 55 + 0.15x Subtract 0.15x from both sides. – 0.15x– 0.15x 1.10x > 55 Divide both sides by 1.10. x > 50 The Spanish club must sell more than 50 bumper stickers to make a profit.

  18. Check It Out! Example 3 A school’s French club is selling bumper stickers. They bought 200 bumper stickers for $45, and they have to give the company 25 cents for every sticker sold. If they plan to sell each bumper sticker for $2.50, how many do they have to sell to make a profit? In order for the French club to make a profit, the revenue must be greater than the cost. 2.5x > 45 + 0.25x

  19. 45 > 2.25x 2.25 2.25 Check It Out! Example 3 Continued 2.5x > 45 + 0.25x Subtract 0.25x from both sides. – 0.25x– 0.25x 2.25x > 45 Divide both sides by 2.25. x > 20 The French club must sell more than 20 bumper stickers to make a profit.

  20. 2 3 3 8 1 4 -10 -9 -8 -7 -6 -5 -4 1 2 3 4 5 6 7 0 -18 -17 -16 -15 -14 -13 -12 1 2 w 3 8 Lesson Quiz: Part I Solve and graph. 1. 4x – 6 > 10 2. 7x + 9 < 3x – 15 3.w – 3w < 32 4.w +  x > 4 x < –6 w > –16

  21. Lesson Quiz: Part II 5. Antonio has budgeted an average of $45 a month for entertainment. For the first five months of the year he has spent $48, $39, $60, $48, and $33. How much can Antonio spend in the sixth month without exceeding his average budget? no more than $42

More Related