Module 7 Review

Solving Equations with variables on both sides

100

solve the following equation:

2x - 1 = x - 3

x = -2 

200

Solve the following equation:

2y + 1 = 3y - 5

y = 6

300

Solve the following equation:

-2y + 3 = 8y - 7

y = 1

400

Country carpets charges $22 per yard and an additional fee of $100. City carpets charges $25 per yard with an additional fee of $70. Write and solve the equation for which the two companies will charge the same. 

x = 10, they will charge the same at 10 yards.

500

Joes canoes charges an initial fee of $20 plus $4 an hour. Callie's canes charges a flat rate of $14 an hour. Find the number of hours for which the total amount for both places charge would be the same. 

x = 2, the charge will be the same at 2 hours. 

Solving equations with rationales

100

5.25x + 3.25 = 1.75x +10.25

x = 2

200

1.9x = 1.3x +37.44

x = 62.4

300

Solve the following equation:

3/4n - 18 = 1/4n - 4

n = 28

400

Solve the following equation:

9+ 3/4x = 7/8x - 10

x =152

500

Solve the following equation:

3/4m + 2 = 2/3m + 5

m = 36

Solving equations using distributive property

100

Solve the following equation:

4(x - 2) = x + 10

x = 6

200

solve the following equation: 

8(12 - k) = 3(k + 21)

k = 3

300

Solve the following equation:

2(x - 6) + 3 = 4 + x 

x = 13

400

Sandra saves 12% of her salary retirement. This year her salary was $3000 more than in the previous year, and she saved $4200. What was her salary the previous year?

Use the equation to solve:

0.12 (x + 3000) = 4200

x = $32,000

her salary in the previous year was $32,000

500

Kyle saves 8% of his income for a new car. This year his salary was $2000 less than in previous year, and he saved $3000. What was his salary the previous year?
Write the equation and solve.

x = 39,500

His salary the previous year was 39,500.

Solving equations with one, many or no solution

100

Solve the equation, determine whether the equation has one, many or no solutions.

4r + 2 = r + 8

r = 2, This equation has one solution. 

200

Solve the equation, determine whether the equation has one, many or no solutions.

2x - 1 = 2x + 3

-1 = 3, this equation has no solutions.

300

Solve the equation, determine whether the equation has one, many or no solutions.

3(y - 2) = 3y - 6

-6 = -6 

This equation has many solutions 

400

Solve the equation, determine whether the equation has one, many or no solutions.

3m + 8 = 3(4 + m) - 4

8=8

This equation has many solutions

500

Solve the equation, determine whether the equation has one, many or no solutions.

3 ( x + 4) + 2 = x + 10

x = -2, 

This equation has one solution.