11-5 solving two-step inequalities course 3 warm up warm up problem of the day problem of the day...
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11-5 Solving Two-Step Inequalities
Course 3
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Warm UpSolve.
1. 6x + 36 = 2x
2. 4x – 13 = 15 + 5x
3. 5(x – 3) = 2x + 3
4. + x =
x = –9
x = –28
x = 6
Course 3
11-5 Solving Two-Step Inequalities
78
316
1116
x = –
Problem of the Day
Find an integer x that makes the following two inequalities true:4 < x2 < 16 and x < 2.5
x = –3
Course 3
11-5 Solving Two-Step Inequalities
Learn to solve two-step inequalities and graph the solutions of an inequality on a number line.
Course 3
11-5 Solving Two-Step Inequalities
Solving a multistep inequality uses the same inverse operations as solving a multistep equation. Multiplying or dividing the inequality by a negative number reverses the inequality symbol.
Course 3
11-5 Solving Two-Step Inequalities
Solve and graph.
Additional Example 1A: Solving Two-Step Inequalities
4x + 1 > 13
4x + 1 > 13 – 1 – 1 Subtract 1 from both sides.
4x > 124x4
> 124
Divide both sides by 4.
x > 3 1 2 3 4 5 6 7
Course 3
11-5 Solving Two-Step Inequalities
Course 3
11-5 Solving Two-Step Inequalities
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
–9x + 7 25
– 7 – 7 Subtract 7 from both sides.
–9x 18
–9x–9
18–9
Divide each side by –9; change to .
x –2-6 -5 -4 -3 -2 -1 0
Course 3
11-5 Solving Two-Step Inequalities
Solve and graph.
Solve and graph.
Check It Out: Example 1A
5x + 2 > 12
5x + 2 > 12 – 2 – 2 Subtract 2 from both sides.
5x > 105x5
> 105
Divide both sides by 5.
x > 2 1 2 3 4 5 6 7
Course 3
11-5 Solving Two-Step Inequalities
–4x + 2 18
–4x + 2 18
– 2 – 2 Subtract 2 from both sides.
–4x 16
–4x–4
16–4
Divide each side by –4; change to .
x –4-6 -5 -4 -3 -2 -1 0
Check It Out: Example 1B
Course 3
11-5 Solving Two-Step Inequalities
Additional Example 2: Solving Inequalities That Contain Fractions
Multiply by LCD, 20.
8x + 15 18
– 15 – 15 Subtract 15 from both
sides.8x 3
Solve + and graph the solution.2x5
34
910
+ 2x5
34
910
20( + ) 20( )2x5
34
910
20( ) + 20( ) 20( )2x5
34
910
Course 3
11-5 Solving Two-Step Inequalities
Distributive Property.
Additional Example 2 Continued
x 38
8x8
38 Divide both sides by 8.
8x 3
0 1
38
Course 3
11-5 Solving Two-Step Inequalities
Check It Out: Example 2
Multiply by LCD, 20.
12x + 5 10
– 5 – 5 Subtract 5 from both
sides.12x 5
Solve + 3x5
14
510
+ 3x5
14
510
20( + ) 20( )3x5
14
510
20( ) + 20( ) 20 ( )3x5
14
510
Course 3
11-5 Solving Two-Step Inequalities
Distributive Property.
Check It Out: Example 2 Continued
x 512
12x12
512 Divide both sides by 12.
12x 5
0 5 12
Course 3
11-5 Solving Two-Step Inequalities
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?
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
Course 3
11-5 Solving Two-Step 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 55 + 0.15x. Substitute the expressions for R and C.
1.25x > 55 + 0.15x Let x represent the number of bumper stickers sold. Fixed cost is $55. Unit cost is 15 cents.
Course 3
11-5 Solving Two-Step Inequalities
Additional Example 3 Continued
– 0.15x – 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 1.10.
1.25x > 55 + 0.15x
1.10x1.10
551.10>
Course 3
11-5 Solving Two-Step Inequalities
Check It Out: Example 3
R > C
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?
Let R represent the revenue and C represent the cost. In order for the French club to make a profit, the revenue must be greater than the cost.
Course 3
11-5 Solving Two-Step Inequalities
Check It Out: 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 45 + 0.25x. Substitute the expressions for R and C.
2.5x > 45 + 0.25x Let x represent the number of bumper stickers sold. Fixed cost is $45. Unit cost is 25 cents.
Course 3
11-5 Solving Two-Step Inequalities
– 0.25x – 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 2.25.
2.5x > 45 + 0.25x
2.25x2.25
452.25>
Check It Out: Example 3 Continued
Course 3
11-5 Solving Two-Step Inequalities
Lesson Quiz: Part I
Solve and graph.
1. 4x – 6 > 10
2. 7x + 9 < 3x – 15
3. w – 3w < 32
4. w +
x < –6
x > 4
Insert Lesson Title Here
w > –1623
14
12
w 38
1 2 3 4 5 6 7
-10 -9 -8 -7 -6 -5 -4
-18 -17 -16 -15 -14 -13 -12
0 38
Course 3
11-5 Solving Two-Step Inequalities
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
Course 3
11-5 Solving Two-Step Inequalities