Some Important points related to Linear Equations

Some Important points related to Linear Equations

  • There is an equality sign in the linear equation. The expression on the left of the equal sign is called the LHS (left-hand side) and the expression on the right of the equal sign is called the RHS (right-hand side).
  • In the linear equation, the LHS is equal to RHS but this happens for some values only and these values are the solution of these linear equations.

Solving Equations which have Linear Expressions on one Side and Numbers on the other Side

There are two methods to solve such type of problems –

1. Balancing Method

In this method, we have to add or subtract with the same number on both the sides without disturbing the balance to find the solution.

Example

Find the solution for 3x – 10 = 14

Solution

Step 1: We need to add 10 to both the sides so that the numbers and variables come on the different sides without disturbing the balance.

3x – 10 +10 =10+14

3x = 24

Step 2: Now to balance the equation, we need to divide by 3 into both the sides.

\mathrm{\dfrac{3x}{3}=\dfrac{24}{3}}

x = 8

So x = 8 is the solution of the equation.

2. Transposing Method

In this method, we need to transpose or transfer the constants or variables from one side to another until we get the solution. When we transpose the terms the sign will get changed.

Example

Find the solution for 2z + 10 = 4.

Solution

Step 1: We transpose 10 from LHS to RHS so that all the constants come in the same side.

2z = 4 -10 (sign will get changed)

2z = -6

Step 2: Now divide both the sides by 2.

\mathrm{\dfrac{2z}{2}=-\dfrac{6}{2}}

z = – 3

So z = -3 is the solution of the equation.

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