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 2x = 1

Denominator of = 2

L.C.M (1, 2) = 2

Therefore, multiplying 2 by 2x and 1 by (x – 1), we get

Now start simplifying it as much as possible. For instance, multiply 2 on both sides,

⇒ (2 × 2x) + (1 × (x – 1)) = 10

⇒ 4x + (x – 1) = 10

⇒ 4x + x – 1 = 10

Constants of the variable can be operated, so

⇒ (4x + x) – 1 = 10

⇒ 5x – 1 = 10

Take the constant 1 on R.H.S. The negative sign on L.H.S will become positive on R.H.S.

⇒ 5x = 10 + 1

⇒ 5x = 11

Divide 5 on both sides to leave x idle.

Thus, we have solved the equation and .