Question

Noah solved an equation as shown below and found that the equation has infinitely many solutions.

-3(x + 4) + 2x = 2(x - 6) - 3x
-3x - 12 + 2x = 2x - 12 - 3x
-x - 12 = -x - 12

Which explains whether Noah is correct?
A. Noah is correct because the two sides of the equation are equivalent expressions.
B. Noah is correct because if he continues the solution, the final solution will be x = - 2
C. Noah is not correct because the equivalent expressions mean that there is no solution.
D. Noah is not correct because he used the distributive property incorrectly.

Answer 1

Option A) Noah is correct because the two sides of the equation are equivalent expressions.

Explanation:

We are given the following information in the question:

`-3(x + 4) + 2x = 2(x - 6) - 3x\\-3x - 12 + 2x = 2x - 12 - 3x\\-x - 12 = -x - 12`

The above equation has infinitely many solutions.

Infinite solution:

If an equation end up with equal values on each side of the equation, then there are infinite solution as for all the values of x the equations would be satisfied.

Noah is correct.

Option A) Noah is correct because the two sides of the equation are equivalent expressions.

Answer 2

A. Noah is correct because the two sides of the equation are equivalent expressions.

EXPLANATION

The equation given to Noah was

`-3(x + 4) + 2x = 2(x - 6) - 3x`

He expanded to get:

`-3x - 12 + 2x = 2x - 12 - 3x`

He then further simplified each side of the equation to get;

`-x - 12 = -x - 12`

Both sides of this equation are equivalent.

Therefore the equation has infinitely many solutions.

The correct answer is A