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Linear Equations in One Variable

    Solving Equations having the Variable on both Sides

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8th class > Linear Equations in One Variable > Solving Equations having the Variable on both Sides

Solving Equations having the Variable on both Sides

An equation is the equality of the values of two expressions. In the equation 2x−3=7, the two expressions are 2x−3 and 7. 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:

Instructions

Solve 2x – 3 = x + 2
We have: 2x = x + 2 + 3
(or) 2x =
(or) 2x – x = x + 5 – x (subtracting x from both sides)
(or) x =

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 + 72 = 3x2-14

5x+72=3x2−14

  • 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.