Question

What is the reason for each step in the solution of the equation? −5(x−6)=10x Drag and drop the reasons into the boxes to correctly complete the table. −5(x−6)=10x −5x+30=10x 30=15x 2=x

Answer 1

Statement Reason

-5(x-6)=10x Given

-5x+30=10x Distributive property

30=15x Addition property of equality

2=x Division property of equality

Explanation:

The given equation is

`-5(x-6)=10x`

We need to find the solutions of given equation.

Using distributive property, we get

`-5(x)-5(-6)=10x`

`-5x+30=10x`

Add 5x on both sides.

`-5x+30+5x=10x+5x` (Addition property of equality)

`30=15x`

Divide both sides by 15.

`(30)/(15)=(15x)/(15)` (Division property of equality)

`2=x`

Therefore, the solution of given equation is x=2.

Answer 2

-5(x -6) = 10x . . . . . given

-5x +30 = 10x . . . . distributive property of multiplication over addition

30 = 15x . . . . . . . . addition property of equality (5x was added to both sides)

2 = x . . . . . . . . . . . division property of equality (both sides were divided by 15)

_____

There is a "property of equality" for any operation you want to do to both sides of the equation: addition, subtraction, multiplication, division, application of a function (such as log or square root or any trig function, for example).

The distributive property lets you add or remove parenthenses according to its rules.

Identity properties of addition and multiplication allow you to add 0 or multiply by 1 anywhere anytime. These operations can take any useful form, such as "completing the square" of a quadratic (by adding and subtracting the same number), changing units [(1 h)/(60 min) = 1, for example], or finding percentages (multiplying by 100%).