Answer :
To show that the equation \(x + 2x - 6 = 0\) can be rearranged to give \(x = \frac{6}{x^2 + 2}\), we need to follow these steps:
1. Combine like terms in the equation \(x + 2x - 6 = 0\) to simplify it.
\(x + 2x - 6 = 0\)
\(3x - 6 = 0\)
2. Add 6 to both sides of the equation to isolate the term with x.
\(3x - 6 + 6 = 0 + 6\)
\(3x = 6\)
3. Divide both sides of the equation by 3 to solve for x.
\(\frac{3x}{3} = \frac{6}{3}\)
\(x = 2\)
4. Substitute the value of x (which is 2) back into the expression \(x = \frac{6}{x^2 + 2}\) to verify the rearranged equation.
\(2 = \frac{6}{2^2 + 2}\)
\(2 = \frac{6}{4 + 2}\)
\(2 = \frac{6}{6}\)
\(2 = 1\)
Therefore, by following the steps above, we can see that the equation \(x + 2x - 6 = 0\) can indeed be rearranged to give \(x = \frac{6}{x^2 + 2}\) when x is equal to 2.
