Question

An equation is shown below:

4(x − 3) − 5(x + 1) = 3

Which statement shows a correct next step in solving the equation?

The equation can become 4x − 3 − 5x + 1 = 3 by applying the associative property of multiplication.

The equation can become 4x − 3 − 5x + 1 = 3 by applying the distributive property.

The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

The equation can become 4x − 12 − 5x − 5 = 3 by applying the associative property of multiplication

Answer 1

Option C is correct.

The equation can become
`4x-12-5x -5 = 3` by applying distributive property.

Explanation:

Given an equation:
`4(x-3)-5(x+1) = 3`

Distributive property states that when a number is multiplied by the sum of two numbers, then the first number can be distributed to both of those numbers and multiplied by each of them separately i.e,,

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

Apply distributive to the given equation we get;

`4 \cdot x -4\cdot 3-5\cdot x -5 \cdot 1 =3`

Simplify:

`4x-12 -5x -5 = 3`

Therefore, the statement which shows a correct next step in solving the equation is, the equation can become
`4x-12 -5x -5 = 3` by applying distributive property.