Module 2 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 load 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: 

20p-185=55

12

300

Solve: 

(5+m)/6=4

19

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

t = -2

200

Solve:

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

a = -6

300

Solve:

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

x = -1

400

Solve: 

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

n = 3

500

Solve: 

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

Identity; infinite solutions

Number of Solutions

100

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

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

-8 = -8

identity/infinitely many solutions

200

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

8(4 - 2x) = 4(3 - 5x) + 4x

32 can not = 12

No solution

300

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

2(3x + 5) = 5(2x - 5) - 4x

10 can not = 25

No solution

400

Finish this equation to make it have No Solution.

3(2x + 4) - x = _____x + _________

5x + (any # except 12)

500

Finish the equation so that you create an equation with infinitely many solutions.

4(x + 2) - 3 = ___________

4x + 5

Square Roots

100

What is the inverse operation of a square power?

square root

200

How many answers does a square root have?

2: one positive and one negative

300

To the nearest tenth, what is the square root of 33?

5.7

400

Solve for x.

5x² - 45 = 0

x = 3, -3

500

Solve for m.

7m² - 5 = 23

m = 2, -2

Cube Roots

100

What is the inverse operation of a cube power?

cube root

200

What is the cube root of 9261

21

300

True or False: There are two answers for cube roots, a positive root and a negative root.

FALSE

That is only true for SQUARE ROOTS

400

My amazon package is in the shape of a cube and has a volume of 15625 units³.

What is one dimension of the box?

s = 25 units

500

Solve the equation for y:

-3(y³ - 3) = 657

y = -6