Addition Property

Question

5(-3x+1)=14(x+1)

Answer 1

Hi Dominic;

5(-3x+1)=14(x+1)

Let's first apply the Distributive Property in Algebra:, and then apply the Addition Property of Equality.

According to this first principle, we can discard the parentheses...

-15x+5=14x+14

According to the Addition Property of Equality, we can add negative 5 to both sides, and the equality of the equation remains...

We want to add -5 to both sides as we proceed to isolate x...

-5+-15x+5=14x+14-5

-15x=14x-9

According to the Addition Property of Equality, we can add negative 14x to both sides, and the equality of the equation remains...

We want to add -14x to both sides as we proceed to isolate x...

-14x-15x=14x-9-14x

-29x=-9

According to the Multiplicative Property of Equality, the two sides of an equation remain equal if they are multiplied by the same number.

Let's multiply both sides by -1/29 to isolate x...

(-1/29)(-29x)=-9(-1/29)

x=-9/29

Answer 2

The addition property of equalities is that if the same number is added to both sides of the equation, it remains equal.

 

The subject equation is:

5(-3x+1)=14(x+1)

 

Distributing the multiplication:

-15x+5=14x+14

 

solving for x:  29x=-19, x=-19/29, would make this equation true. 

 

Adding a 3 to both sides

 

-15x+8=14x+17 and solving for x, x=-25/29

 

The addition property does not hold for this equality.

 

 

If determining whether the addition property is satisfied is not the question, please clarify what information is needed.