7th - Multi-Step Inequalities

One-Step Inequalities

Equations with Parentheses

Equations with Variables on Both sides

WORD PROBLEMS YEAHHHHHH

Multi-Step Inequalities

100

Graph the following inequality. x < 16

100

3(6 - y) = 27

What is y = -3

100

9x - 10 = 5x + 14

4x - 10 = 14

4x = 24

x = 6

100

Mr. T buys a giant box of Cocoa Pebbles at Costco. The box provides enough delicious Cocoa Pebbles for 46 bowls. If Mr. T eats three bowls of delicious Cocoa Pebbles each week, how many weeks have to pass before there are only 22 bowls of sweet, sweet Cocoa Pebbles left?

46 - 3x = 22

-3x = -24

x = 8 weeks

100

x/4 - 6 ≤ -10

x/4 ≤ -4

x <= -16

200

8 > p - 4

What is p < 12

200

4(d + 7) = 16

d = -3

200

-3x - 13 = -7x + 15

4x - 13 = 15

4x = 28

x = 7

200

Bill weighs 110 pounds and is gaining ten pounds each month. Phil weighs 152 pounds and is losing 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil?

110 + 10m = 152 - 4m

14m + 110 = 152

14m = 42

m = 3 months

200

3g + 12 > 5g - 8

12 > 2g - 8

20 > 2g

10 > g

OR g < 10

300

1/3x>=-4

x >= -12

300

8 + 5(n - 6) = 27 + (-2n)

8 + 5n - 30 = 27 - 2n

5n - 22 = 27 - 2n

7n - 22 = 27

7n = 49

n = 7

300

-15x = -5(3x + 7) + x

-15x = -15x - 35 + x

-15x = -14x - 35

-x = -35

x = 35

300

Container A and container B have leaks. Container A has 800 ml of water, and is leaking 6 ml per minute. Container B has 1000 ml, and is leaking 10 ml per minute. How many minutes, m, will it take for the two containers to have the same amount of water?

800 - 6m = 1000 - 10m

4m + 800 = 1000

4m = 200

m = 50 minutes

300

2(14 - 3r) < -4r

28 - 6r < -4r

28 < 2r

14 < r

or r > 14

400

-0.025x ≤ -4

x >= 160

400

-7k - (10 - k) = -58

-7k - 10 + k = -58

-6k - 10 = -58

-6k = -48

k = 8

400

-9m + 16 + 8m= -5m - 4(m + 4)

-9m + 16 + 8m = -5m - 4(m + 4)

-9m + 16 + 8m = -5m - 4m - 16

-m + 16 = -9m - 16

8m = -32

m = -4

400

Wendy has two kids, Dan and Erin. Wendy is three years younger than three times Erin's age, and Dan is 4 years older than Erin. If the sum of Dan's and Erin's is 38, how old is Wendy?

Erin: x

Wendy: 3x - 3

Dan: x + 4

x + x + 4 = 38

2x + 4 = 38

2x = 34

x = 17 <--Erin

Wendy = 3(17) - 3 = 51 - 3 = 48

400

-8 > (3x)/7 + 4

-12 > (3x)/7

-84 > 3x

-28 > x

x < -28

500

-100 < -20x

What is

x<5

500

What is the value for x if the perimeter of a triangle is 29 units and its sides are 7, x, and x + 2?

7 + x + x + 2 = 29

2x + 9 = 29

2x = 20

x = 10

500

-3y - (10y - 25) = 6(-3y -10)

-3y - 10y + 25 = -18y - 60

-13y + 25 = -18y - 60

5y + 25 = -60

5y = -85

y = -17

500

During a pandemic, toilet paper apparently is a hot commodity in stores. Jim checks the local stores' stocks, and notes that Walmart has twice as many rolls of tp than Target, and Sam's Club has eight less than three times what Walmart has. If the sum of Target's and Walmart's inventory is ten less than Sam's Club's inventory, how many rolls of tp does Target have?

Target: x

Walmart: 2x

Sam's Club: 3(2x)-8 = 6x - 8

x + 2x = 6x - 8 - 10

3x = 6x - 18

-3x = -18

x = 6 <-- Target

500

-3(y - 1) > 12 - y + 3

-3y + 3 > 12 - y + 3

-3y + 3 > -y + 15

-2y > 12

y < -6