Pre-Algebra 10-4 Solving Multistep Inequalities 10-4 Solving Multistep Inequalities Pre-Algebra HOMEWORK & Learning Goal HOMEWORK & Learning Goal Lesson Presentation Lesson Presentation AIMS Prep AIMS Prep

Pre-Algebra 10-4 Solving Multistep Inequalities Pre-Algebra HOMEWORK Page 517 #14-26 EVENS

Pre-Algebra 10-4 Solving Multistep Inequalities Our Learning Goal Students will be able to solve multi-step equations with multiple variables, solve inequalities and graph the solutions on a number line.

Pre-Algebra 10-4 Solving Multistep Inequalities Our Learning Goal Assignments Learn to solve two-step equations. Learn to solve multistep equations. Learn to solve equations with variables on both sides of the equal sign. Learn to solve two-step inequalities and graph the solutions of an inequality on a number line. Learn to solve an equation for a variable. Learn to solve systems of equations.

Pre-Algebra 10-4 Solving Multistep Inequalities Warm Up Solve. 1. 6x + 36 = 2x 2. 4x – 13 = x 3. 5(x – 3) = 2x x = x = –9 x = –28 x = 6 Pre-Algebra 10-4 Solving Multistep Inequalities x = –

Pre-Algebra 10-4 Solving Multistep Inequalities Problem of the Day Find an integer x that makes the following two inequalities true: 4 < x 2 < 16 and x < 2.5 x = –3

Pre-Algebra 10-4 Solving Multistep Inequalities Today’s Learning Goal Assignment Learn to solve two- step inequalities and graph the solutions of an inequality on a number line.

Pre-Algebra 10-4 Solving Multistep Inequalities Solving a multistep inequality uses the same inverse operations as solving a multistep equation. THE DIFFERENCE IS……. Multiplying or dividing the inequality by a negative number reverses the inequality symbol.

Pre-Algebra 10-4 Solving Multistep Inequalities Solve and graph. Additional Example 1A: Solving Multistep Inequalities A. 4x + 1 > 13 4x + 1 > 13 – 1 – 1Subtract 1 from both sides. 4x > 12 4x4x 4 > 12 4 Divide both sides by 4. x >

Pre-Algebra 10-4 Solving Multistep Inequalities Solve and graph. Try This: Example 1A A. 5x + 2 > 12 5x + 2 > 12 – 2 – 2Subtract 2 from both sides. 5x > 10 5x5x 5 > 10 5 Divide both sides by 5. x >

Pre-Algebra 10-4 Solving Multistep Inequalities Additional Example 1B: Solving Multistep Inequalities B. – 7 < 3x + 8 – 7 < 3x + 8 – 8 – 8Subtract 8 from both sides. – 15 < 3x – 15 3 < 3x 3x 3 Divide both sides by 3. –5 < x

Pre-Algebra 10-4 Solving Multistep Inequalities B. – 5 < 2x + 9 – 5 < 2x + 9 – 9 – 9Subtract 9 from both sides. – 14 < 2x – 14 2 < 2x 2x 2 Divide both sides by 2. –7 < x Try This: Example 1B

Pre-Algebra 10-4 Solving Multistep Inequalities Additional Example 1C: Solving Multistep Inequalities C. -9x + 7  25 –9x + 7  25 – 7 – 7Subtract 7 from both sides. –9x  18 –9x –9  18 –9 Divide each side by –9; change  to . x  –2x  –

Pre-Algebra 10-4 Solving Multistep Inequalities C. -4x + 2  18 –4x + 2  18 – 2 – 2Subtract 2 from both sides. –4x  16 –4x –4  16 –4 Divide each side by –4; change  to . x  –4x  – Try This: Example 1C

Pre-Algebra 10-4 Solving Multistep Inequalities Solve and graph. Additional Example 2A: Solving Multistep Inequalities A. 10x + 21 – 4x < –15 10x + 21 – 4x < –15 – 21 – 21Subtract 21 from both sides. 6x6x 6 < –36 6 Divide both sides by 6. x < – x + 21 < –15 Combine like terms. 6x < –36

Pre-Algebra 10-4 Solving Multistep Inequalities Solve and graph. Try This: Example 2A A. 15x + 30 – 5x < –10 15x + 30 – 5x < –10 – 30 – 30Subtract 30 from both sides. 10x 10 < –40 10 Divide both sides by 10. x < – x + 30 < – 10 Combine like terms. 10x < –40

Pre-Algebra 10-4 Solving Multistep Inequalities Additional Example 2B: Solving Multistep Inequalities Multiply by LCD, 20. 8x + 15  18 – 15 – 15 Subtract 15 from both sides. 8x  3 B. +  2x  2x2x ( + )  20 ( ) 2x2x ( ) + 20 ( )  20 ( ) 2x2x

Pre-Algebra 10-4 Solving Multistep Inequalities Additional Example 2 Continued x  3 8  8x8x Divide both sides by 8. 8x 

Pre-Algebra 10-4 Solving Multistep Inequalities Try This: Example 2B Multiply by LCD, x + 5  10 – 5 – 5 Subtract 5 from both sides. 12x  5 B. +  3x  3x3x ( + )  20 ( ) 3x3x ( ) + 20 ( )  20 ( ) 3x3x

Pre-Algebra 10-4 Solving Multistep Inequalities Try This: Example 2B Continued x  5 12  12x 12 5 Divide both sides by x 

Pre-Algebra 10-4 Solving Multistep Inequalities Additional Example 2C: Solving Multistep Inequalities C. 8x + 8 > 11x – 1 8x + 8 > 11x – 1 – 8x – 8x Subtract 8x from both sides. 8 > 3x – > 3x 3x 3 Add 1 to each side. 3 > x > 3x Divide both sides by 3.

Pre-Algebra 10-4 Solving Multistep Inequalities Try This: Example 2C C. 4x + 3 > 8x – 1 4x + 3 > 8x – 1 – 4x – 4x Subtract 4x from both sides. 3 > 4x – > 4x 4x 4 Add 1 to each side. 1 > x > 4x Divide both sides by 4.

Pre-Algebra 10-4 Solving Multistep Inequalities Additional Example 3: Business 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? Let R represent the revenue and C represent the cost. In order for the Spanish club to make a profit, the revenue must be greater than the cost. R > C

Pre-Algebra 10-4 Solving Multistep Inequalities Additional Example 3 Continued The revenue from selling x bumper stickers at $1.25 each is 1.25x. The cost of selling x bumper stickers is the fixed cost plus the unit cost times the number of bumper stickers sold, or x. Substitute the expressions for R and C. 1.25x > x Let x represent the number of bumper stickers sold. Fixed cost is $55. Unit cost is 15 cents.

Pre-Algebra 10-4 Solving Multistep Inequalities Additional Example 3 Continued – 0.15x Subtract 0.15x from both sides. 1.10x > 55 x > 50 The Spanish club must sell more than 50 bumper stickers to make a profit. Divide both sides by x > x 1.10x >

Pre-Algebra 10-4 Solving Multistep Inequalities Try This: Example 3 R > C A school’s Spanish 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? Let R represent the revenue and C represent the cost. In order for the Spanish club to make a profit, the revenue must be greater than the cost.

Pre-Algebra 10-4 Solving Multistep Inequalities Try This: Example 3 Continued The revenue from selling x bumper stickers at $2.50 each is 2.5x. The cost of selling x bumper stickers is the fixed cost plus the unit cost times the number of bumper stickers sold, or x. Substitute the expressions for R and C. 2.5x > x Let x represent the number of bumper stickers sold. Fixed cost is $45. Unit cost is 25 cents.

Pre-Algebra 10-4 Solving Multistep Inequalities – 0.25x Subtract 0.25x from both sides. 2.25x > 45 x > 20 The Spanish club must sell more than 20 bumper stickers to make a profit. Divide both sides by x > x 2.25x > Try This: Example 3 Continued

Pre-Algebra 10-4 Solving Multistep Inequalities Don’t forget your proper heading! Trade & Grade! 10-4 Lesson Quiz: Part 1 Solve and graph. 1. 4x – 6 > x + 9 < 3x – w – 3w < w +  x < –6 x > 4 w > – w w 

Pre-Algebra 10-4 Solving Multistep Inequalities Lesson Quiz: Part 2 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

6 th Grade AIMS Prep Recall some test-taking tricks that you use to “win” on the AIMS Math. Use at least one to solve the following example!

AIMS Example 2