Equations and Inequalities

Solving Equations

100

Solve the following equation:

4 - 8x=13x + 2(2 + x)

x = 0

200

Solve the following equation:

-(7 - 4x) = 9

x = 4

300

Solve the following equation:

3(5x - 2) - 6x = 3(3x + 2)

No Solution

400

Solve the following equation:

3(-3x + 4) = 15 - 11x + 2x - 3

Infinitely Many Solutions

500

Solve the following equation:

-5(1 - 5x) + 5(-8x - 2) = -4x - 8x

x = -5

Equations with Rational Coefficients

100

Solve the following equation: 

(3/2)x = 14

x = 7

200

0.4x + 6 = 0.15x

x = -24

300

Solve the following equation: 

7x/4 - 3/2 = -5

x = -2

400

Solve the following equation: 

(4x - 3)/6 + 1/3 = x/2

x = 1

500

Solve the following equation: 

(-2x+1)/3 - (x+3)/7 = 8

x = -10

Solving Inequalities

100

Solve the following inequality:

x + 15 > 27

x > 12

200

Solve the following inequality:

5x + 7 ≤ -23

x ≤ -6

300

Solve the following inequality:

13 + 4x ≥ 3(x + 13)

x > 26

400

Solve the following inequality:

2(-8 - x) - 15 ≤ 9

x ≥ -20

500

Solve the following inequality:

28 - x ≥ 7(x - 4)

x ≤ 7

More Equations and Inequalities Inequalities

100

Solve the following equation:

(4/3)x = 12

x = 9

200

Solve the following equation:

7x + 20 < -15

x < -5

300

Solve the following equation: 

x/4 - x/6 = 2/3

x = 4

400

Solve the following inequality:

-5x/3 + 4/3 > -8/9

x < -4/3

500

Solve the following inequality:

-x/3 - x/5 ≤ 4

x ≥ -7.5

Inequality Word Problems

100

Solve this problem by writing and solving an inequality. Define your variable.

Manny needs to buy 5 work shirts that are each the same price and a sweater for $20. He can spend more than than $70. What is the maximum amount that each shirt can cost?

x = cost of the shirt ($)

5x + 20 ≤ 70

Each shirt can cost at most $14.

200

Solve this problem by writing and solving an inequality. Define your variable.

Ricky has $18.00. Bagels cost $1.10 each and a small container of cream cheese costs $1.50. What is the greatest number of bagels Ricky can buy if he also buys one small container of cream cheese?

x = # of bagels Ricky can buy

1.1x + 1.5 ≤ 18

Ricky can buy a maximum of 15 bagels.

300

Solve this problem by writing and solving an inequality. Define your variable.

Jake has $50 to spend at Adventureland. He wants to get funnel cake while he is there, which costs $4 each. How many funnel cakes can Jake buy to still have at least $35 to spend on rides and games?

x = # of funnel cakes Jake can buy

4x + 35 ≤ 50

x ≤ 3.75

Jake can buy 3 funnel cakes.

400

Solve this problem by writing and solving an inequality. Define your variable.

The 35 members of a drill team are trying to raise at least $1,200 to cover travel costs to a training camp. They have already raised $500. How much money should each member raise to meet the goal?

x = amount of money each member should raise ($)

35x + 500 ≥ 1,200

Each member should raise at least $20.

500

Solve this problem by writing and solving an inequality. Define your variable.

Molly saved $150 from her job to buy books. She goes to the store and buys books that cost $9.40 each. What is the maximum number of books Molly can buy to still have $9 left over to buy lunch?

x = # of books Molly buys

150 - 9.40x ≥ 9

Molly can buy a maximum of 15 books.