The linear equation is.

Fractions with different denominators can not be added. So, write the equation with common denominator.

Find the least common denominator L.C.M.

Multiples of 7 = 7, 14, 21, 28, 35, 42, ......

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, .........

Least Common Multiple of 7 and 6 is 42

Write the left hand side equation with common denominator

Since denominators are same add the numerators over the denominator

Multiply each side by 42.

Cancel common terms.

Apply distributive properties : .

Subtract 1596x from each side. \ \

Apply Additive Inverse Property: a + (-a) = 0.

Group like terms.

Combine like terms.

Divide each side by negative 1550.

Cancel common terms.

.

The solution is .

Check :

Substitute the value of in given linear equation. \ \

.

The above statement is true.

So, is the solution of .