## Input Interpretation

The chemical equation given is:

*CH3CO2H + Al(OH)3 → Al(C2H3O2)3 + H2O*

This equation represents the reaction between acetic acid and aluminum hydroxide, which produces aluminum acetate and water.

## Balanced Equation

To balance the chemical equation algebraically, we need to add stoichiometric coefficients to the reactants and products. Let's assume the coefficients to be c1, c2, c3, and c4 for CH3CO2H, Al(OH)3, Al(C2H3O2)3, and H2O, respectively.

*c1CH3CO2H + c2 Al(OH)3 → c3Al(C2H3O2)3 + c4H2O*

Now, let's set the number of atoms in the reactants equal to the number of atoms in the products for C, H, O, and Al:

*C: 2c1 = 6c3*

*H: 4c1 + 3c2 = 9c3 + 2c4*

*O: 2c1 + 3c2 = 6c3 + c4*

*Al: c2 = c3*

Since the coefficients are relative quantities and underdetermined, we choose a coefficient to set arbitrarily. To keep the coefficients small, the arbitrary value is ordinarily one. For instance, we set c2 = 1 and solve the system of equations for the remaining coefficients:

*c1 = 3*

*c2 = 1*

*c3 = 1*

*c4 = 3*

Substitute the coefficients into the chemical reaction to obtain the balanced equation:

Answer:

The balanced equation for the given chemical reaction is:

*3 CH3CO2H + Al(OH)3 → Al(C2H3O2)3 + 3 H2O*