Solving Linear Equations in One Variable

Linear Equations in One Variable can easily be solved by following the steps discussed below,

• Step 1: Write the given equation in standard form and if a or b is a fraction then take the LCM of the fraction to make them integers.

• Step 2: The constants are then taken to the right side of the equation.

• Step 3: All the variables and the constant terms are then simplified to form one single variable term and one single constant.

• Step 4: The coefficient of the variable is made 1 by dividing both sides with a suitable constant to get the final result.

Let’s understand the above steps with the help of the following example.

Examples on Linear Equation in One Variable

Solve the following linear equation in one variable.

Example: Solve 3x + 1/2 = (1/2)x – 13/2

Solution:

Step 1: Arranging in standard form and taking LCM

3x – (1/2)x + 1/2 + 13/2 = 0

⇒ (6x – x + 2 + 13)/2 = 0

⇒ 6x – x + 2 + 13 = 0

Step 2: Transposing the constant to the right-hand side

6x – x = -2 – 13

Step 3: Simplification

5x = -15

Step 4: Make coefficient of x to 1

Dividing both sides by 5 we get,

5x/5 = -15/5

x = -3

This is the required solution.

Linear equation in one variable is the equation that is used in algebra for finding unknown quantities. It is used for representing the conditions that are dependent on one variable. It is a linear equation i.e. the equation in which the degree of the equation is one, and it only has one variable.

Let’s know more about Linear Equations in one Variable in detail below.