Solve Equations with Variables on both Sides Worksheet

**Page 1**

1.

When 2 is multiplied by 2, it produces the same result as when 2 is added to 2. It is 4 in both cases. Can you think of another pair of numbers with the same arithmetical feature?

a. | 3, 3 | ||

b. | 1.5, 1.5 | ||

c. | 3, 4.5 | ||

d. | 3, 1.5 |

By trail and error, substitute the value of

Substitute

Substitute

Substitute

3 + 1.5 = 3 × 1.5

4.5 = 4.5

[The condition of equality satisfies.]

Therefore, another pair of numbers that satisfies the arithmetic feature is 3, 1.5.

Correct answer : (4)

2.

Solve: 3$x$ = 12 - $x$

a. | 2 | ||

b. | 3 | ||

c. | 1 | ||

d. | 6 |

[Original equation.]

4

[Add

[Divide each side by 4.]

[Simplify.]

The solution of the equation is

Correct answer : (2)

3.

Solve:

- 3$x$ + 56 = 5$x$ + 24

a. | 3 | ||

b. | 5 | ||

c. | 8 | ||

d. | 4 |

[Original equation.]

- 3

[Add 3

56 = 8

[Combine the like terms.]

56 - 24 = 8

[Subtract 24 from each side.]

32 = 8

[Simplify.]

[Divide each side by 8.]

[Simplify.]

Correct answer : (4)

4.

Find the value of $y$ in the equation 6$y$ - 2 = $y$ + 13 .

a. | 6 | ||

b. | 8 | ||

c. | 3 |

[Original equation.]

6

[Subtract

5

[Combine like terms.]

5

[Add 2 on both sides.]

5

[Combine like terms.]

[Divide each side by 5.]

[Simplify.]

Correct answer : (4)

5.

Which of the following choices is the first step in solving the equation - 2$x$ = - 32 + 19$x$?

a. | Add - 2$x$ on both sides | ||

b. | Multiply 2 on both sides | ||

c. | Subtract 19$x$ on both sides | ||

d. | None of the above |

[Original equation.]

To have the like terms on one side, first we have to subtract 19

Correct answer : (3)

6.

A Library provides two types of cards for their members: a red card, which costs $24 plus $4.25 rent per book, and a yellow card, which costs $18 plus $5.75 rent per book. For what number of books do both the cards cost the same?

a. | 4 | ||

b. | 6 | ||

c. | 3 | ||

d. | 5 |

24 + 4.25

[Write an equation.]

24 + 4.25

[Subtract 18 on both sides.]

6 + 4.25

[Combine like terms.]

6 + 4.25

[Subtract 4.25

6 = 1.5

[Simplify.]

[Divide by 1.5 on both sides.]

4 =

[Simplify.]

So, for 4 books both cards cost the same.

Correct answer : (1)

7.

Two trucks, loaded with cargo, start from Amsterdam. The first truck leaves Amsterdam traveling at a steady rate of 50 miles per hour and is 150 miles behind the second truck that travels at a steady rate of 80 miles per hour. What is the time taken by the second truck to catch up to the first truck?

a. | 5 hours | ||

b. | 7 hours | ||

c. | 9 hours | ||

d. | None of the above |

Speed of the second truck x

80

[Original equation.]

80

[Subtract 50

30

[Combine like terms.]

[Divide each side by 30.]

[Simplify each side.]

The second truck will catch up to the first truck in 5 hours.

Correct answer : (1)

8.

Solve: 2$t$ - 4 + 45$t$ = - 2$t$ + 45

a. | 4 | ||

b. | 2 | ||

c. | 1 | ||

d. | None of the above |

[Original equation.]

47

[Combine like terms.]

47

[Add 2

49

[Simplify.]

49

[Add 4 to each side.]

49

[Simplify each side.]

[Divide each side by 49.]

[Simplify.]

Correct answer : (3)

9.

Which of the following equations has the solution of $b$ = 5?

a. | 4b+2a = 2b - 8 | ||

b. | 3b - 18 - b = -b - 3 | ||

c. | 17b + 5b - 2a = 7b + 8 | ||

d. | -2b - 2a + 3b = 2b - 4 |

Consider choice B, 3

[Original equation.]

2

[Combine like terms.]

2

[Add

3

[Simplify.]

3

[Add 18 to each side.]

3

[Combine like terms.]

[Divide each side by 3.]

[Simplify.]

Correct answer : (2)

10.

Solve the equation 4($x$ + 2) = 4$x$ + 8 and determine whether it has one solution, no solution, or is an identity.

a. | One solution | ||

b. | No solution | ||

c. | Identity | ||

d. | None of the above |

[Given equation.]

4

[Multiply 4 to remove the paranthesis.]

4

[Subtract 4

8 = 8

[Combine like terms.]

So, the equation is an identity.

Correct answer : (3)