Question

a student says that if 5x2 = 20, then x must be equal to 2. do you agree or disagree with the student? justify your answer.

Answer 1

I disagree. If each side of the equation is divided by 5, the result is x2 = 4. By the square root property of equality, x = -2 or x = 2. So x could be -2 instead of 2.

Answer 2

To check if the student is correct, we are going to solve the equation step by step.

Step 1 divide both sides of the equation by 5:

`5x^2=20`

`(5x^2)/(5) =(20)/(5)`

`x^2=4`

Step 2 take square root to both sides of the equation:

`√(x^2) =(+/-)√(4)`

`x=(+/-)√(4)`

`x=2` or
`x=-2`

The equation has tow solutions,
`x=2` and
`x=-2`.

I disagree with the student because
`x=2` is just one solution and not the only one;
`x=-2` is also a valid solution of the equation.