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Solving Equations Having the Variable on Both Sides

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Solving Equations Having the Variable on Both Sides:

In this type of problem, we need to bring all the constants on one side and all the terms having variables on the other side. Then they can be solved easily.

Solve: 2x – 3 = x + 2

Solution:  

We have, 2x - 3 = x + 2

or 2x = x + 2 + 3

or 2x = x + 5

or 2x - x = x + 5 - x    .....(subtracting x from both sides)

or  x = 5                      ......(solution) 

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. Also, note that subtracting x from both sides amounts to transposing x to LHS.

Example

Solve: 5x + `7/2 = 3/2x` - 14

5x + `7/2 = 3/2x` - 14

Multiply both sides of the equation by 2. We get

`2 xx (5x + 7/2) = 2 xx (3/2x - 14)`

`(2 xx 5x) + (2 xx 7/2) = (2 xx 3/2x) - (2 xx 14)`

or 10x + 7 = 3x - 28

or 10x - 3x + 7 = -28   .....(transposing 3x to LHS)

or 7x + 7 = -28

or 7x = -28 - 7

or 7x = -35

or `x = (-35)/7`

or x = -5.

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