Algebra I Unit 2

Creating Equations

100

Jenny has 7 marbles and Kenny has 5. How many do they have together? Let x be the total number of marbles. 

x = 7 + 5

x = 12

200

A number x is squared, tripled, halved and then increased by 12. After all this the equation equals 6.

3x²/2 + 12 = 6

300

You want to buy x bags of chips. Each bag is 2 dollars, and you have 24 dollars to spend. 

2x = 24

400

Helen has 2 inches of hair cut off each time she goes to the hair salon. If h equals the length of hair before she cuts it and c equals the length of hair after she cuts it, which equation would you use to find the length of Helen's hair after she visit the hair salon?

c = h - 2

500

Jenny, Kenny, and Penny together have 51 marbles. Kenny has double as many marbles as Jenny has, and Penny has 12. How many does Jenny have?

n + 2n + 12 = 51

3n + 12 = 51

Solving Two Step Equations

100

2x -1 = 3

Solve for x.

x = 2

200

6x +18 = 24

Solve for x.

x = 1

300

(1/7) x +7 = 9

Solve for x.

x = 14

400

(2/3)x - 1 = 5

Solve for x.

x = 9

500

(7/5)x - 12 = -5

Solve for x

x = 5

Solving Multi-Step Equations

100

4x + 1 = 2x + 3

Solve for x. 

x = 1

200

2x - 4 = x + 6

Solve for x.

x = 10

300

-2(x + 6) = 2

Solve for x.

x = -7

400

6x - 5 = x/2

Solve for x.

x = 10/11

500

3x² + 2 = 29

Solve for x.

x = 3

Solving Inequalities

100

x + 3 > 7

Solve the inequality. 

x > 4

200

2x < -8

Solve the inequality.

x < -4

300

3x - 5 > x - 3

Solve the inequality.

x > 1

400

x/3 < 2x - 4

Solve the inequality.

x > 12/5

500

2x² - 5 < 21

Solve the inequality.

x < sqrt(13)

Solving Systems of Equations

100

x + y = 4

x - y = 6

x = 5

y = -1

(5,-1)

200

2x + y = 4

8x - y = 6

x = 1 

y = 2

(1,2)

300

4x + y = 6

-2x - y = 12

x = 9

y = - 30

(9, -30)

400

3x + y = 8

x + 2y = 1

x = 3

y = -1 

(3,-1)

500

2x + 4y = 8 

-5x + 4y = 1

x = 1

y = 3/2

(1,3/2)