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Method of Solving an Equation

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definition

Transposing: Transposing means moving to the other side. When you transpose a number from one side of the equation to the other side, you change its sign.

notes

Methods of Solving an Equation:

Method 1:

  • We carry out a series of identical mathematical operations such as adding, subtracting, multiplying, or dividing on the two sides of the equation in such a way that on one of the sides we get just the variable.
  • The last step is the solution of the equation.

Example,

`x/5 + 7 = - 3`

`x/5 + 7 – 7 = - 3 – 7`

`x/5 = - 10`

`x/5(5) = - 10(5)`

x = 50.

Method 2:

  • Transposing means moving to the other side. Transposition of a number has the same effect as adding the same number to (or subtracting the same number from) both sides of the equation.
  • When you transpose a number from one side of the equation to the other side, you change its sign.
  • We can carry out the transposition of an expression in the same way as the transposition of a number.

For example,
5x + 12 = 27

Transposing + 12.........(On transposing + 12 becomes – 12)

5x = 27 – 12

5x = 15

x = 3.

Example

Solve: 4(m + 3) = 18

Let us divide both sides by 4.

m + 3 = `18/4`

m + 3 = `9/2`

m = `9/2 – 3`..............(transposing 3 to RHS)

m = `3/2`.

Example

Solve: – 2(x + 3) = 8.

– 2(x + 3) = 8

We divide both sides by (– 2), so as to remove the brackets in the LHS, we get,

x + 3 = `8/(- 2)`

x + 3 = – 4
x = – 4 – 3...........(transposing 3 to RHS)

x = – 7..................(required solution)

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