Module 3 Review

Writing and Interpreting

100

Write an equation for the sentence:

The quotient of 24 and x is the same as the difference of 14 and 2 times x.

x/24 = 14-2x

200

Translate the equation into a sentence:

2b-10=4

10 less than the product of 2 and a number b is the same as 4.

300

Translate the sentence into an equation:

The product of three and b less than one hundred is the same as six times b.

100-3b=6b

400

Write an equation from the sentence:

The product of six and the sum of a number x and nine equals two times x subtracted from four.

6(x+9)=4-2x

500

Anthony has saved $35 of the $140 he needs to purchase a new bicycle. He plants to save $15 each week, w, until he has enough money to buy the bicycle. Write an equation to find the number of weeks it will take Anthony to save enough money to buy the bicycle.

35+15w=140

Solving One Step Equations

100

Solve the equation: 

36+x=-63

-99

200

Solve the equation: 

-5d=65

-13

300

Solve the equation:

m/15=-6

-90

400

9=-3/2z

-6

500

Margo is repaying a loan from her parents. She has already paid $315 and still owes them $1245. Write and solve an equation to find the original amount, a, of the loan.

a-315=1245; $1560

Solving multi-step equations

100

Use inverse operations to solve each equation. Check your solution.

43=8z+11

4

200

Solve this equation: 

−g+2(3+g)=−4(g+1)

g = -2

300

Solve:

 −8−x=−3(2x−4)+3x

x = 10

400

Solve: 

x/4+18=9

-36

500

The distance from Pablo's house to a mall is 1 more mile than 5 times the distance from his house to his school. The distance from Pablo's house to the mall is 16 miles. Write and solve an equation to find the distance from Pablo's house to his school.

5d+1=16; 3 mi

Solving equations with variables on Each side

100

Solve the equation: 

-t+7=3t+15

-2

200

Solve:

-5(-a-1)=3a-7

-6

300

Solve:

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

-1

400

Solve: 

(2n+2)/8=n/3

3

500

Solve: 

9y+8=4(y+2)+5y

Identity; infinite solutions

Number of Solutions

100

What type of solution is

a = a

identity/infinitely many solutions

200

Solve the equation and state whether it has one solution, no solution, or identity/infinitely many solutions.

3x + 4 = 3x

no solution

300

Solve the equation and state whether it has one solution, no solution, or identity/infinitely many solutions.

3(6 - 4g) = -2(6g - 9)

18 = 18

Infinitely many solutions

400

Solve the equation and state whether it has one solution, no solution, or identity/infinitely many solutions.

3(a + 3) - 2 = 1/3(9a - 6)

7 does not = -6

No Solution

500

Finish the equation so that it creates an equation with no solution.

5 + 7(y - 2) = ____y + _______

7y - 9 = 7y + 9