PROPERTIES OF EQUALITY WORKSHEET

Problem 1 : 

Solve for x. Name the property used in each step.

7x - 2  =  4x + 13

Problem 2 : 

Solve for y. Name the property used in each step.

-y/5  =  3

Problem 3 : 

Solve for x. Name the property used in each step.

3(x - 2)  =  2x + 8

Problem 4 : 

Solve for y. Name the property used in each step.

52y - 3(12 + 9y)  =  64

Problem 5 : 

Solve for x. Name the property used in each step.

(3x + 2) / 5  =  2

Problem 6 : 

Solve for m. Name the property used in each step.

4m/5 - 7/4  =  m/5 + m/4

Problem 7 :

In the diagram above, AB  =  CD. Prove AC  =  BD.  

Problem 8 : 

Find m∠4 using the following information. 

m∠1 + m∠2  =  66°

m∠1 + m∠2 + m∠3  =  99°

m∠3  =  m∠1

m∠1  =  m∠4

Answers

1. Answer :

Given :

7x - 2  =  4x + 13

Subtraction Property of Equality : 

Subtract 4x from each side. 

3x - 2  =  13

Addition Property of Equality : 

Add 2 to each side. 

3x  =  15

Division Property of Equality : 

Divide both sides by 2. 

x  =  5

2. Answer :

Given :

-y/5  =  3

Multiplication Property of Equality : 

Multiply each side by 5.

-y  =  15

Multiplication Property of Equality : 

Multiply each side by (-1).

y  =  -15

3. Answer :

Given :

3(x - 2)  =  2x + 8

Distributive Property : 

Distribute 3 to x and 2. 

3x - 6  =  2x + 8

Subtraction Property of Equality : 

Subtract 2x from each side of the equation.

x - 6  =  8

Addition Property of Equality : 

Add 6 to each side. 

x  =  14

4. Answer :

Given :

52y - 3(12 + 9y)  =  64

Distributive Property :

Distribute 3 to 12 and 9y. 

52y - 36 - 27y  =  64

Simplify :

25y - 36  =  64

Addition Property of Equality : 

Add 36 to each side. 

25y  =  100

Division Property of Equality : 

Divide both sides by 25. 

y  =  4

5. Answer :

Given :

(3x + 2) / 5  =  4

Multiplication Property of Equality : 

Multiply each side by 5.

3x + 2  =  20

Subtraction Property of Equality : 

Subtract 2 from each side. 

3x  =  18

Division Property of Equality : 

Divide each side by 3. 

x  =  6

6. Answer :

Given :

4m/5 - 7/4  =  m/5 + m/4

The least common multiple of the denominators (4, 5) in the equation is 

=  4 x 5

=  20

Multiplication Property of Equality : 

Multiply each side by 20.

20(4m/5 - 7/4)  =  20(m/5 + m/4)

Distributive Property : 

20(4m/5) - 20(7/4)  =  20(m/5) + 20(m/4)

Simplify. 

16m - 35  =  4m + 5m

16m - 35  =  9m

Subtraction Property of Equality : 

Subtract 9m from each side. 

7m - 35  =  0

Addition Property of Equality : 

Add 35 to each side. 

7m  =  35

Division Property of Equality : 

Divide each side by 7.

m  =  5

7. Answer :

Given :

AB  =  CD

Addition Property of Equality : 

Add BC to each side. 

AB + BC  =  CD + BC

  AB + BC  =  BC + CD ------(1)

By segment addition postulate, we have

AC  =  AB + BC -----(2)

BD  =  BC + CD -----(3)

Substitution Property of Equality : 

Substitute (2) and (3) in (1). 

(1) -----> AC  =  BD

8. Answer :

Given :

m∠1 + m∠2  =  66°

m∠1 + m∠2 + m∠3  =  99°

Substitution Property of Equality : 

66° + m∠3  =  99°

Subtraction Property of Equality : 

Subtract 66° from each side.

m∠3  =  33°

Given :

m∠3  =  m∠1,  m∠1  =  m∠4

Transitive Property of Equality : 

m∠3  =  m∠4

Subtraction Property of Equality : 

m∠4  =  33°

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