Question

Consider the sequence of steps to solve the equation:

5(x - 3) = 7

Step 1 = 101x - 3) = 7x

Step 2 = 10x - 30 = 7x

Step 3 = 3x - 30 = 0

Step 4 = 3x = 30

Step 5 = x= 10

Identify the property of equality which yields Step 3.

Answer 1

The subtraction and Addition properties of equality are used in the given step 3 equation.

Explanation:

Given equation is
`5(x-3)=(7x)/(2)`

To identify the property of equality used in step 3 of the given equation :

`5(x-3)=(7x)/(2)`

`2(5(x-3))=7x`

Also given their solved steps as below

Step 1 : 10(x-3) = 7 x (by using the Multiplication property of equality)

10x+10(-3)=7x

Step 2: 10 x - 30 = 7 x ( by using the Distributive property )

10x-7x-30=7x-7x

Step 3: 3 x - 30=0 (by using the subtraction and Addition properties of equality)

3x-30+30=0+30

Step 4: 3x = 30

`x=(30)/(3)`

Step 5: x=10

∴ In step 3 we are using the subtraction and Addition properties of equality.