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Linear Equation in One Variable

Linear equation in one variable

Linear equation in one variable:

Earlier, we learnt about algebraic expression and algebraic equation. It is clear about the difference between algebraic expression and algebraic equation that algebraic equation involves equality and on the other hand there is no equality involved in algebraic expression.

Let’s clear it by seeing the examples:

Algebraic expressions are: 2x, 2x + 5, 8xy – 3, 7xy
Algebraic equations are: 4x = 7, 2x + 5 = y, 3x +2 = 8xy

Linear expression:

We can say linear expression as the algebraic expression which has only single degree on its variables.
As: 2x, 3y + 5 etc.

Linear Equation:

We denote linear equation the algebraic equation in which the highest power on the variables is equal to one.
Example: 2x + 3 = 0, 5x -2 = 0, 3x – y = z

Now it is clear that the linear equation can be of many types when number of variables is counted. In this section we will read only the linear equation where only one variable is involved.

Linear equation in one variable:

As we have seen that algebraic equation has equality involved in it. The same is in linear equation. There are two parts in these equations, the symbol of equality separates them. One part is LHS (left Hand Side) and the other side is RHS (Right Hand Side).

Any linear equation in one variable containing equations on both side, we solve it simply transposing the variables or literals on one side and the numeral on the other side. You can solve any linear equations involving a single variable by simply transposing like to like side.

In some cases, the algebraic equation is not a linear equation but after simplification, it converts into linear equation in one variable then it becomes easy to solve. We will have to identify for the given equation that if it can be simplified or not.

There are many applications of linear equation in one variable in everyday life. We can clearly see its uses in calculating numbers, ages, currency, perimeters and several other parameters.

Examples on linear equation in one variable:

  1. Solve 2x + 4 = 8.
    Solution:
    As, 2x + 4 = 8
    when we subtract 4 from both side there will be no impact on its equality.
    2x + 4 – 4 = 8 – 4
    2x = 4
    now we divide each side by 2
    x = 2
  2. What number should we add to twice the number 7 to get 30?
    Solution:
    Let us assume the number be x
    7 + x = 30
    let’s subtract 7 from both side
    7 + x – 7 = 30 – 7
    x = 23
    The required number is 23
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