Question

Identify the property used in the first four steps to solve the equation 4(x-7)=2x-6 4x-28=2x-6 2x-28=-6 2x=22 x=11 the answer choices for each step are Distributive, addition property of equality and multiplication property of equalityd,a,a,m

Answer 1

Step 1: Distributive Property

Step 2: Addition Property of Equality

Step 3: Addition Property of Equality

Step 4: Multiplication Property of Equality

Explanation:

Answer 2

The reason of each steps are Distributive property, addition property of equality, addition property of equality and multiplication property of equality.

Explanation:

Let a,b and c are real number.

According to distributive property

`a\cdot (b+c)=a\cdot b+a\cdot c`

Where, a,b and c are real number.

According to addition property of equality
`a=b` and
`a+c=b+c` are equivalent equations.

According to multiplicative property of equality
`a=b` and
`ac=bc` are equivalent equations.

The given equation is

`4(x-7)=2x-6`

`4(x)+4(-7)=2x-6`

`4x-28=2x-6` (Distributive Property)

Add -2x both sides.

`4x-28-2x=2x-6-2x`

`2x-28=-6` (Addition property of equality)

Add 28 both sides.

`2x-28+28=-6+28`

`2x=22` (Addition property of equality)

Multiply both sides by
`(1)/(2)`

`2x* (1)/(2)=22* (1)/(2)`

`x=11` (Multiplication property of equality)