Question

Examine the equation. 4(x – 3) = 4x – 12 Which of the following is true? (Check all that apply.) It is a true statement. Any input will result in an equivalent equation. It is equivalent to an equation of the form a = a. It has no solution. Only one input will result in a true statement.

Answer 1

It is a true statement.

Any input will result in an equivalent equation.

It is equivalent to an equation of the form a = a.

Answer 2

A, B, and C.

Explanation:

We have the equation:

`4(x-3)=4x-12`

Let’s distribute the left. This yields:

`4x-12=4x-12`

Let’s add 12 to both sides:

`4x=4x`

And subtract 4x from both sides:

`0=0`

We get the true statement 0=0.

Hence, A is correct.

Because it is a true statement, any input will yield an equivalent output.

Hence, B is also correct.

We also have the form a=a, where a is 0.

Hence, C is also correct.

Therefore, our correct answers are A, B, and C.