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

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:

$5x^2=20$

$\frac{5x^2}{5} =\frac{20}{5}$

$x^2=4$

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

$\sqrt{x^2} =(+/-)\sqrt{4}$

$x=(+/-)\sqrt{4}$

$x=2$ 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.

Answer 2

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.