# Solving Equations having the Variable on both Sides

**An equation is the equality of the values of two expressions.** In the equation **In most examples that we have come across so far, the RHS is just a number**.

But this need not always be so; **both sides could have expressions with variables**. **For example:** the equation **2x – 3 = x + 2** has expressions with a variable on both sides; the expression on the LHS is (2x – 3) and the expression on the RHS is (x + 2).

We now discuss how to solve such equations which have expressions with the variable on both sides.

**Example 1:**

**Solve 2x – 3 = x + 2**

Here we subtracted from both sides of the equation, not a number (constant), but a term involving the variable. **We can do this as variables are also numbers**.

**Note that subtracting x from both sides amounts to transposing x to LHS.**

**Example 2:**

**Solve 5x + **

- Multiply both sides of the equation by
. - Now further expand on both sides of the equation.
- On simplifying further
- Now, transposing 3x to LHS (subtract it from both sides)
- Now, we have one term on either side.
- Now, we get the value of x =
- Thus, x =
is the solution.