Let’s solve the equations below:

This is an algebraic equation which is univariate as it contains only one variable, that is, x.

We have

We need to solve this equation.

That is, we need to find the value of variable x.

We will use any kind of mathematical operation (addition, subtraction, multiplication or division) in order to find x.

Here, we can simplify the equation by taking L.C.M of the denominators on L.H.S of the equation.

Denominator of = 5

Denominator of = 7

L.C.M (5, 7) = 35

Therefore, multiplying 7 by x and 5 by 2, we get

Now, simplify it as much as possible. Cross multiplying, 35 by x and 10 by (7 × x) + (5 × 2), we get

⇒ 10 × ((7 × x) + (5 × 2)) = 35 × x

⇒ 10 × (7x + 10) = 35x

By distributive law, multiply 10 by 7x and by 10.

⇒ (10 × 7x) + (10 × 10) = 35x

⇒ 70x + 100 = 35x

Take x’s on one side and constants on the other. Here, shift 35x on L.H.S (positive sign of 35 will become negative) and 100 on R.H.S (positive sign of 100 will become negative).

⇒ 70x – 35x = -100

⇒ 35x = -100

Divide 35 on both sides to leave x idle.

Thus, we have solved the equation and .