Equations & Inequalities

Graphing System of Equalities

100

Graph the following system of equations AND indicate the type of solution.

y = 3x - 3

y = 3x + 2

Parallel lines = NO SOLUTION

200

Graph the following system of equations AND indicate the type of solution.

y = 2x + 5

y = 2x + 5

MANY SOLUTIONS

300

Graph the following system of equations AND indicate the type of solution.

y = -5/3x + 3

y = 1/3x - 3

ONE SOLUTION

(3 , -2 ) 

400

Graph the inequality AND shade

y > -3x + 2

- Dotted line

- Shade above

500

Graph the inequality AND shade

y ≤ 2x - 4

- solid line

- shade below

Draw on a Number Line

100

x>5

open circle on 5 and shaded to the right

200

x≥-3

closed circle on -3 and shaded to the right

300

X+5≤9

closed circle on 4, shade to the left

400

-1< x-7

Open circle on negative 8 and shade to the right

500

4-x≤7

Closed circle on negative 3 and shade to the right

Solving one-step inequalities

100

x-5>7

X>12

200

x-3≤-8

x≤-5

300

3x<9

x<3

400

-3x>-12

x<4

500

-10>-2x

x>5

Solving two-step inequalities

100

2x+3>7

x>2

200

5x-8≥ -18

x≥-2

300

3<2x+7

x>-2

400

6≥7-x

x≥1

500

-6x-7<29

x>-6

Real-world problems

100

Suppose you earn $6.15 per hour working part time at a dry cleaner. Write and solve an inequality to find how many full hours you must work to earn at least $100.

6.15h ≤ 100

h: hours

EXPLANATION: you must work full 16 hours to earn at least $100. 

200

The cost of a gallon of orange juice is $3.50. What is the maximum number of containers you can buy for $15?

3.50g ≥  15

g: gallons

EXPLANATION: You can buy 4 containers for $15. 

300

Daniel had no more $25 to spend at the fair. If the admission to the fair is $4 and the rides cost $1.50 each, what is the greatest number of rides Daniel can go on?

4 + 1.50r ≤ 25

r: rides

EXPLANATION: Daniel can go on 14 rides. 

400

Stan earned $7.55 per hour plus an additional $100 in tips waiting tables on Saturday evening.  He earned $160 in all.  To the nearest hour, what is the least number of hours Stan would have to work to earn this much money?

7.55h + 100 ≥ 160

h: hours

EXPLANATION: To the nearest hour, Stan would  have to work at least 8 hours to earn $160.

500

Connor went to the carnival with $22.50.  He bought a hot dog and a drink for $3.75, and he wanted to spend the rest of his money on ride tickets which cost $1.25 each.   What is the maximum number of ride tickets that he can buy?

3.75 + 1.25r ≤  22.50

r: number of rides

EXPLANATION: Connor can buy a maximum of 15 ride tickets.