NAME THE PROPERTY USED IN EACH STEP

Problem 1 :

Fill in the reason that justifies each step.

Given: AC = 36

AB + BC = AC ______

3x + 2x + 1 = 36 ______

5x + 1 = 36 ______

5x = 35 ______

x = 7 ____

Solution:

Given:

AB + BC = AC

The length of AB is 3x and length of BC is 2x + 1

Substitution Property:

Using substitution property, applying the values of AB and BC.

3x + 2x + 1 = 36

Addition Property:

Using addition property adding the like terms,

5x + 1 = 36 

Subtraction Property:

Using subtracting property, subtracting 1 on both sides,

5x = 35 

Division Property:

Using division property, divide by 5 on both sides,

x = 7

So, the value of x is 7.

Problem 2 :

Solve the equation and state the reason for each step.

5(2x - 1) = 9x + 4

Solution:

Given:

5(2x - 1) = 9x + 4

Distributive Property:

Distribute 5 to 2x and 1.

10x - 5 = 9x + 4

Subtraction Property:

Subtract 9x from each side of the equation.

x - 5 = 4

Addition Property:

Add 5 to each side.

x = 9

Problem 3 :

In the diagram at the right, m∠WPY = m∠XPZ. Complete the argument to show that m∠WPX = m∠YPZ.

Solution :

Step 1 :

m∠WPX = m∠WPY + m∠YPX ---(1)

Substituting the value of m∠WPX,

Here m∠WPX is the sum of m∠WPY and m∠YPX

Step 2 :

m∠YPZ = m∠YPX + m∠XPZ ---(2)

Substituting the value of m∠YPZ,

Here ∠YPZ is the sum of m∠YPX and m∠XPZ

Step 3 :

With the given 

m∠WPY = m∠XPZ

Using addition property, adding m∠YPX on both sides.

m∠WPY + m∠YPX = m∠YPX + m∠XPZ

Step 4 :

Using reflexive property, from step 1 and step 2

m∠WPX = m∠YPZ

Problem 4 :

Which properties are missing in the steps to solve the equation:

76 = 5x - 15 + 2x

Solution:

Problem 5 :

Fill in the missing properties and equation in the steps to solve the equation

5x + 3(x + 4) = 28?

Solution:

Identify the property of equality that justifies each missing step or equation in each of the following tables.

Problem 6 :

Solution:

Problem 7 :

Solution:

Problem 8 :

Solution:

Problem 9 :

Solution: