Question

Han was looking at the equation 6x−4+2(5x+2)=16x. He said, “I can tell right away there are no solutions, because on the left side, you will have 6x+10x and a bunch of constants, but you have just 16x on the right side.” Do you agree with Han? Explain your reasoning.

Answer 1

No, I don't agree with Han because there are infinitely many solutions to the equation.

Explanation:

We have been given an equation
`6x-4+2(5x+2)=16x`. Han said, “I can tell right away there are no solutions, because on the left side, you will have
`6x+10x` and a bunch of constants, but you have just
`16x` on the right side.”

We are asked to determine whether Han is right or not.

First of all, we will simplify left side of our given equation as:

`6x-4+2\cdot 5x+2\cdot 2=16x`

`6x-4+10x+4=16x`

`6x+10x+4-4=16x`

`16x=16x`

Since both sides of equation are equal, so any value of x will make the equation true.

Therefore, there will be infinitely many solution of the equation.

Answer 2

No, Han is not correct.

Explanation:

In order to question the reasoning of Han, we can start by solving this equation.

6x - 4 + 2(5x + 2) = 16x

Collecting the like terms together and the constant together, we will obtain:

6x + 10x - 16x = 4 - 4

0 *x = 0

This equation has got infinitely many solutions that whatever number you put to the place of x, you will always have zero.

So that, Han's reasoning was not correct.