During the combustion of methane,CH4,shown by: CH4(g) + O2(g)-->CO2(g) + H2O(g), what is the balanced equation?

CH4(g) + O2(g)-->CO2(g) + H2O(g)

When you balance out an equation you get the same amount of each element on both sides of the equation.

In this problem we have 1 carbon on both sides, 4 hydrogen on the right and 2 on the left, and 2 oxygens on the left and 3 on the right side.

We need to balance out the hydrogens therefore we add a two to make it equal:

CH4(g) + O2(g)-->CO2(g) + 2H2O(g)

Now we have 1 carbon, and 4 hydrogen on both sides but 2 oxygen on the left and 4 on the right, so we have to balance that out.

We do so by putting in another 2:

CH4(g) + 2O2(g)-->CO2(g) + 2H2O(g)

Now we have 1 carbon, 4 oxygen, and 4 hydrogen.

It is now balanced.