# SOLVING EQUATIONS WORKSHEET

Problem 1 :

Solve :

x + (-11) = -25

Problem 2 :

Solve :

8y = -24

Problem 3 :

-11 + y = 9

Given the above equation, find the value of

20 - (11 - y)

Problem 4 :

If 33 - x = x + 27 - 5x, what is the value of (33 + 3x)?

Problem 5 :

If (1/2)x + 3 = 3/4 - x, what is the value of x?

Problem 6 :

Solve the following equation :

x - (3 - 2x) + (4 - 5x) = -7

Problem 7 :

(4/5)(x - 5) - (1/5)(x - 10) = 19

Problem 8 :

If three quarters of a number decreased by twenty is equal to eighty two, what is that number?

Problem 9 :

There are one hundred forty-two students in a high school band. These students represent two ninth of the total students in the high school. Find the total number of students in the school.

Problem 10 :

The quotient of a number and five equals nine less than one half of the number. What is the number?

Problem 11 :

(1/3)(15 - 6x) = 5 - kx

If the linear equation above is an identity, what is the value of k?

Problem 12 :

(1/3)(9 - 6x) = 5 - kx

If the linear equation above has no solution, find the value of k.

x + (-11) = -25

x + (-11) + 11 = -25 + 11

x = -14

8y = -24

Divide both sides by 8.

8y/8 = -24/8

y = -3

-11 + y = 9

y = 20

The value of 20 - (11 - y) :

20 - (11 - y) = 20 - (11 - 20)

= 20 - (-9)

= 20 + 9

= 29

33 - x = x + 27 - 5x

33 - x = 27 - 4x

33 + 3x = 27

Subtract 33 from both sides.

3x = -6

Divide both sides by 3.

x = -2

The value of (33 + 3x) :

33 + 3x = 33 + 3(-2)

= 33 - 6

= 27

(1/2)x + 3 = 3/4 - x

x/2 + x + 3 = 3/4

Subtract 3 from both sides.

x/2 + x = 3/4 - 3

(x + 2x)/2 = (3 - 12)/4

3x/2 = -9/4

Multiply both sides by 2.

3x = -18/4

3x = -9/2

Divide both sides by 3.

x = -9/6

x = -3/2

x - (3 - 2x) + (4 - 5x) = -7

x - 3 + 2x + 4 - 5x = -7

-2x + 1 = -7

Subtract 1 from both sides.

-2x = -8

Divide both sides by -2.

x = 4

(4/5)(x - 5) - (1/5)(x - 10) = 21

Multiply both sides of the equation by 5 to get rid of the denominators.

4(x - 5) - 1(x - 10) = 95

Use Distributive property.

4x - 20 - x + 10 = 95

3x - 10 = 95

3x = 105

Divide both sides by 3.

x = 35

Let x be the number.

(3/4)x - 20 = 82

3x/4 - 20 = 82

3x/4 = 102

Multiply both sides by 4.

3x = 408

Divide both sides by 3.

x = 136

The number is 136.

Let x be the total number of students in the school.

(2/9)x = 142

Multiply both sides by 9.

2x = 1278

Divide both sides by 2.

x = 639

The total number of students in the school is 639.

Let x be the number.

x/5 = (1/2)x - 9

x/5 = x/2 - 9

In the equation above, we find two different denominators 5 and 2.

The least common multiple of (2, 5) is 10.

Multiply both sides of the above equation by 10 to get rid of the denominators.

10(x/5) = 10(x/2 - 9)

2x = 10x/2 - 90

2x = 5x - 90

Subtract 5x from both sides.

-3x = -90

Divide both sides.

x = 30

The number is 30.

If an equation is an identity, then it will have infinitely many solution.

(1/3)(15 - 6x) = 5 - kx

Use Distributive Property.

5 - 2x = 5 - kx

Subtract 5 from both sides.

-2x = -kx

Multiply both sides by -1.

2x = kx

In the equation above, if k = 2,

2x = 2x

The above equation is true for all values of x, hence it is an identity.

So, the given equation is an identity when k = 2.

(1/3)(9 - 6x) = 5 - 2x

Use Distributive Property.

3 - 2x = 5 - kx

In the equation above, if k = 2,

3 - 2x = 5 - 2x

3 = 5

(false statement)

So, the given equation has no solution when k = 2.

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