Solving Equations with Variables on both Sides Worksheet

**Page 1**

1.

Paul wants to go to Atlanta from San Francisco. He is comparing the rental plans of two companies. Henry Car Rentals charges $110 per week plus 60 cents per mile . William Car Rentals charges $90 per week plus 64 cents per mile. Find the number of miles for which the rental charges of the two companies are the same.

a. | 825 miles | ||

b. | 600 miles | ||

c. | 500 miles | ||

d. | 679 miles |

Weekly charges for hiring car from Henry Car Rentals for

Weekly charges for hiring car from William Car Rentals for

110 + 0.6

[Equate the rental charges.]

20 = 0.04

500 =

[Solve for

So, the car rental charges for the two companies are same for 500 miles.

Correct answer : (3)

2.

Solve:

20$y$ - 7$y$ + 15 = 8$y$ + 30

a. | 3 | ||

b. | 2 | ||

c. | 5 | ||

d. | 4 |

[Original equation.]

13

[Combine like terms.]

13

[Subtract 15 from each side.]

13

[Simplify both sides.]

13

[Subtract 8

5

[Simplify both sides.]

[Simplify.]

Correct answer : (1)

3.

Solve: $\frac{j}{9}$ + 14.93 = 9($j$ - 2)

a. | 6.7 | ||

b. | 7.7 | ||

c. | 3.7 | ||

d. | 5.7 |

[Original equation.]

[Use distributive property.]

[Add 18 to both sides.]

[Combine like terms.]

(

[Multiply each side by 9.]

[Simplify.]

[Subtract

296.37 = 80

[Simplify.]

[Divide each side by 80.]

[Simplify.]

Correct answer : (3)

4.

Solve 4$x$ = 50 - $x$.

a. | 13 | ||

b. | 8 | ||

c. | 10 | ||

d. | 9 |

[Original equation.]

5

[Add

[Divide each side by 5.]

[Simplify.]

The solution of the equation is

Correct answer : (3)

5.

Solve:

- 2$x$ + 55 = 8$x$ + 35

a. | 4 | ||

b. | 1 | ||

c. | 3 | ||

d. | 2 |

[Original equation.]

- 2

[Add 2

55 = 10

[Combine the like terms.]

55 - 35 = 10

[Subtract 35 from each side.]

20 = 10

[Simplify.]

[Divide each side by 10.]

[Simplify.]

Correct answer : (4)

6.

Solve the equation.

4$y$ - 3 = $y$ + 3

a. | 7 | ||

b. | 1 | ||

c. | 3 | ||

d. | 2 |

[Original equation.]

4

[Subtract

3

[Combine like terms.]

3

[Add 3 to both sides.]

3

[Combine like terms.]

[Divide each side by 3.]

[Simplify.]

Correct answer : (4)

7.

Choose the first step that would help you solve the equation - 7$x$ = - 35 + 20$x$.

a. | add - 7$x$ to both sides | ||

b. | subtract 20$x$ from both sides | ||

c. | multiply both sides by 7 | ||

d. | divide both sides by 7 |

[Original equation.]

To have the like terms on one side, first we need to subtract 20

Correct answer : (2)

8.

A library provides two types of cards for its members. A red card that costs $48 plus $4.25 rent per book and a yellow card costs $36 plus $5.75 rent per book. Find the number of books for which both cards would cost the same.

a. | 9.3 | ||

b. | 8 | ||

c. | 1 | ||

d. | 10.5 |

48 + 4.25

[Write an equation.]

48 + 4.25

[Subtract 36 on both sides.]

12 + 4.25

[Combine like terms.]

12 + 4.25

[Subtract 4.25

12 = 1.5

[Simplify.]

[Divide by 1.5 on both sides.]

8 =

[Simplify.]

So, for 8 books both cards cost the same.

Correct answer : (2)

9.

Solve the equation, 2($x$ + 3) = 2$x$ + 6 and determine whether it has one solution, no solution, or is an identity.

a. | an identity | ||

b. | not enough information given | ||

c. | one solution | ||

d. | no solution |

[Given equation.]

2

[Multiply 2 to remove the paranthesis.]

2

[Subtract 2

6 = 6

[Combine like terms.]

So the equation is an identity.

Correct answer : (1)

10.

Solve the equation 2($x$ + 9) = 2$x$ + 6 and determine whether it has one solution, no solution or is an identity.

a. | not enough information given | ||

b. | one solution | ||

c. | no solution | ||

d. | an identity |

[Original equation.]

2

[Distribute 2.]

2

[Subtract 2

18 ¹ 6

[Combine like terms.]

The equation 18 = 6 is never true. So, the original equation has no solution.

Correct answer : (3)