The equation is .

The L.C.D of 1,6 is 6. \ \

Rewrite the equation .

Subtract 35 from each side.

Group terms with common factors.

Factor the G.C.F from each grouping.

Combine like terms using distributive property: .

Apply zero product property: If ab = 0 then a = 0, b = 0.

First .

Apply addition property of equality: If a = b then a + b = b + a.

Add 5 to each side.

Apply additive inverse property: .

Divide each side by 2. \ \

Second .

Apply subtraction property of equality: If a = b then a b = b a.

Subtract 7 from each side.

Apply additive inverse property: .

Divide each side by 3.

Check:

To check the solution substitute  in .

The L.C.D of 4,12 is 12.

The first solution is true.

To check the solution substitute in .

Product of two same sings is positive.

The L.C.D of 9,18 is 18.

The second solution is true.

The values of .