# Solve Equation Worksheet

Solve Equation Worksheet
• Page 1
1.
Find the value of n, if n + 7 = 17.
 a. 10 b. 9 c. 11 d. 12

#### Solution:

n + 7 = 17

n = 17 - 7 = 10

2.
Find the value of $y$ in the equation $y$ + 2 = 4 by using algebra tiles.
 a. 7 b. 3 c. 6 d. 2

#### Solution:

The model for the linear equation is
[One y-tile and two 1-tiles on the left side and four 1-tiles on the right side.]

[Isolate the variable.]

[Remove two 1-tiles from both sides to show the value of y.]

The value of y is 2.

3.
Find the value of $y$ from the algebra tiles.

 a. 6 b. 2 c. 8 d. 4

#### Solution:

In the model, the left hand side contains one variable y-tile and four -1 tiles, the right hand side has two +1 tiles.

The linear equation for the model is y - 4 = 2
[Four -1 tiles represent -4 and two 1 tiles represent 2.]

y - 4 + 4 = 2 + 4
[Add 4 on each side to isolate the variable y.]

y = 6
[Add 4 and 2 to get 6.]

So, the value of the variable y is 6.

4.
Find the value of $y$ in the equation $y$ - 3 = 4 using the algebra tiles.
 a. 4 b. 7 c. 6 d. 3

#### Solution:

y - 3 = 4
[Original Equation.]

Model the equation using algebra tiles.
[One y-tile and three -1-tiles on left side and four +1-tiles on right side.]

[Add three 1-tiles on both sides, to make zero pairs to isolate the variable tile.]

Isolate the variable tile.

The value of y is 7.
[Seven 1-tiles represent +7.]

5.
Find the value of $y$ in the equation $y$ - 3 = - 7 by using the algebra tiles.
 a. -5 b. -6 c. -4 d. -9

#### Solution:

[Model the equation in the form of algebra tiles.]

[Isolate the common constant tiles from both sides.]

[Remove isolated tiles from both sides.]

The value of y = -4.

6.
Find the value of $y$ in the equation $y$ + 2 = 2, by using algebra tiles.
 a. 4 b. 6 c. 1

#### Solution:

[Model the equation in the form of algebra tiles.]

[Add two negative tiles on both sides.]

[Remove the zero pairs on both sides.]

The value of y is 0.
[No tiles on the right side represent 0.]

7.
Two packets of rice together weigh 5 kg. If one packet weighs 2 kg, then what is the weight of the other packet? Solve using algebra tiles.
 a. 3 kg b. 2 kg c. 5 kg d. 9 kg

#### Solution:

Let y be the weight of the other packet.

y + 2 = 5
[Write the algebraic equation for the total weight of the two packets.]

Represent the equation in the form of algebra tiles.
[One variable tile and two 1-tiles on the left side and five 1-tiles on the right side.]

[Isolate the variable tile by subtracting two 1-tiles on each side.]

[Remove the grouped 1-tiles to show the value of y.]

So, the weight of the other packet is 3 kg.
[Three 1-tiles represent 3 kg.]

8.
Find the height of Rebecca using algebra tiles, if the total height of Rebecca and Nancy is 11 feet and the height of Nancy is 5 feet.
 a. 6 feet b. 7 feet c. 4 feet d. 8 feet

#### Solution:

Let y be the height of Rebecca.

5 + y = 11
[Write the algebraic equation for the total height of Rebecca and Nancy.]

Represent the equation in the form of algebra tiles.
[One variable tile and five 1-tiles on the left side and eleven 1-tiles on the right side.]

[Isolate the variable tile by subtracting five 1-tiles from each side.]

[Remove the grouped 1-tiles to show the value of variable.]

So, the height of Rebecca is 6 feet.

9.
Dennis and his son caught 6 fish. If Dennis caught 4 fish, then how many fish did his son catch? Solve using algebra tiles.
 a. 2 b. 3 c. 6 d. 4

#### Solution:

Let y be the number of fish caught by Dennis's son.

The equation for the total number of fish caught by Dennis and his son is 4 + y = 6
[Write the linear equation.]

Represent the equation in the form of algebra tiles.
[One variable tile and four 1-tiles on left side and six 1-tiles on the right side.]

[Make a group of four 1-tiles on each side to isolate the variable tile.]

[Remove the grouped 1-tiles on both sides to show the value of variable y.]

The number of fish caught by Dennis's son is 2.

10.
Solve for $x$.
$\frac{x}{2}$ = 1
 a. 1 b. 2 c. $\frac{1}{2}$

#### Solution:

x2 = 1
[Original equation.]

x = 1 × 2
[Multiply both sides with 2.]

x = 2
[1 × 2 = 2.]

So the value of x is 2.