7th Grade Equations and Inequalities

Distributive Property

100

Expand 5(2y−3)

10y - 15

200

Factor −9c−12

-3(3c + 4)

300

Expand -7(2b−3)

-14b +21

400

Factor 5b²+10b

5b(b +2)

500

Factor 21a - 14b + 35

7(3a - 2b + 5)

Solving Equations

100

4x + 5 = 17

x = 3

200

x/7 + 3 = 8

x=35

300

(x+3)/5 = 8

x = 37

400

2(3x + 6) = 30

x = 3

500

-4( 2x + 4) = -56

x=5

Simplifying Expressions

100

10y - 4y + 2

6y + 2

200

5(b - 2) + 3b

8b - 2

300

4c + 2(c + 1) - 6

6c - 5

400

7f - (5 -3f)+3f

13f - 5

500

(1/2)(4g - 6) + (2/3)(9g + 12) - 5g

3g + 5

Solving Inequalities

100

2x + 11 > 23

x > 6

200

5x - 9 < 11

x < 4

300

x/2 + 6 >= 13

x>= 14

400

-3x + 9 > 36

x < -9

500

-5x - 12 > 23

x < -7

Real-world Scenarios

100

Sara charges a fee of $30 and $5 an hour to tutor people in math. If she made $80, how many hours did she work?

Write an equation for this situation.

5x + 30 = 80 or 30 + 5x = 80

200

A cable company charges $50 per visit and $20 for each device they install. If you owe $130 how many devices did you get?

Write an equation for this situation.

50 + 20x = 130 or

20x + 50 = 130

300

Sarah earns $20 an hour and already has $100 saved. When will she have more than $300?

Write an inequality for this situation.

20x + 100 > 300

400

A teacher can have no more than 30 students in the class. If they already have 9, how many more students can join?

Write an inequality for this situation. 

x + 9 <= 30

500

Tickets to a show cost $7 each and parking is $8. A group of friends can spend no more than $50. How many tickets can they buy? 

Write an inequality to represent this situation.

7x + 8 <= 50