Question

Explain why dividing each side of \small 3x^2=6x by \small 3x is not a reliable way to solve the equation.

Answer 1

See Explanation

Explanation:

Given

`3x^2 = 6x`

Required

Why dividing by
`3x` is not reliable

The reason is that, the given expression is a quadratic equation and as such, it will most likely have two solutions.

So, when the expression is divided by
`3x`, the solution will be
`x = 2`, leaving out the other possible solution.

The right way is:

`3x^2 = 6x`

Subtract 6x from both sides

`3x^2 - 6x = 6x - 6x`

`3x^2 - 6x = 0`

Factorize

`3x(x - 2) = 0`

Split

`3x = 0\ or\ x - 2 = 0`

Solve for x in both cases:

`x = 0\ or\ x = 2`