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

Warm Up Response ~$

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

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.

Solve and graph. Additional Example 1A: Solving Two-Step Inequalities 4x + 1 > 13 – 1 – 1Since 1 is added to 4x, subtract 1 from both sides. 4x > 12 4x4x 4 > 12 4 Since x is multiplied by 4, divide both sides by 4. x >

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

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

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

Check It Out! Example 1A 5x + 2 > 12 – 2 – 2Subtract 2 from both sides. 5x > 10 5x5x 5 > 10 5 Divide both sides by 5. x >

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

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

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 > x

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 >

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 > x

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

Lesson Quiz: Part I Solve and graph. 1. 4x – 6 > x + 9 < 3x – w – 3w < w +  x < –6 x > 4 w > – w w 

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