Solving and Graphing Linear Inequalities

Single Variable Inequalities

100

Double points x - 7 > 16

solve for x

x > 23

200

-4x < 24

x > -6

300

2x + 8 > -12

x > 10

400

-5(3 - x) + 21 < -3x + 14

x < 1

500

DOUBLE POINTS An electronic store makes $125 profit on every Earpod it sells and $100 profit on every Beats headphones they sell. The store owner wants to make a profit of at least $500 a day selling earpods and Beats headphones. Write a linear inequality to determine the number of Earpods and Beats headphones the owner needs to sell to meet his goal.

125x + 100y > 500

Standard Form

100

What is the y-intercept for the following equation?

x-y=3

y=-3

200

What is the x-intercept for the following equation?

x-y=3

x = 3

300

DOUBLE POINTS What is the slope for the following equation?

x-y=3

m = 1

400

What is the y-intercepts, and slope for the following equation?

3x-2y=-10

y= 5, m = 3/2

500

DOUBLE POINTS What is the y-intercepts, and slope for the following equation?

3x + 4y=4

y=1, m=-3/4

Random

100

DOUBLE POINTS h(t) = -t + 2; Find h(-2)

h(-2) = 4

200

g(x) = 3x - 1; Find g(7)

g(7) = 20

300

DOUBLE POINTS 

g(x) = 3x - 1; Find g(x)=5

x = 2 

400

DOUBLE POINTS John threw a Superbowl party and ordered pizzas and breadsticks. The breadsticks were $4 each and the pizza was $11 each. With at least 25 people coming John spent at least $180. If he ordered a minimim of 20 item, how many of each food items did he get?

16 pizzas and 6 breadsticks

500

graph y<2

horizontal dotted line at y=2, shaded below

Inequalities

100

What type of line does < have?

dashed

200

What type of line does < have?

Solid

300

DOUBLE POINTS What type of line and where do you shade for the term "at least"?

solid line and shade above

400

How would the line for the following look and where are the solutions located?

y< 3x-7

solid line and the solutions are located below the line

500

How would the line for the following look and where are the solutions located?

y> 4x

dashed and above the line

Graphing

100

Is (-2, 3) a solution to 2x - y > -9?

YES; -7 > -9

200

How do you graph the following y > -x + 8?

Dashed line, shade above, y-intercept=8 and the slope is -1

300

DOUBLE POINTS How do you graph the following: y < 2/3 x - 4

dashed line, shade below, b=-4, m=2/3

400

How do you graph the following: x > -2

dashed, right, vertical line

500

How do you graph the following: Shade in the solution sets 

y > 2x + 1

y < -3x - 1

solid, above is shaded, positive slope line

dotted line, below is shaded, negative slope