HW # 78 - p. 150 & 151 # 1-54 even Warm up

7 13 1 16 16 8 x = – Week 23, Day Three HW # 78 - p. 150 & 151 # 1-54 even Warm up Solve. Graph the solution. 1.6x + 36 = 2x 2. 4x – 13 = 15 + 5x 3. 5(x – 3) = 2x + 3 4. + x = x = –9 x = –28 x = 6 You need to do your audit TODAY!

Warm Up Response ~$

Homework Check p. 146 & 147 # 1-44 even

Goals for Today • 3-8 Solving Two-Step Inequalities • Examples and Notes from p. 148 & 149 • CW: Inequalities Worksheet A

Extra slides for practice

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.

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

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.

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

 -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

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

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.

 -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

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

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.

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

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.

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

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

HW # 78 - p. 150 & 151 # 1-54 even Warm up