# Linear Equations With Fractions

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Linear equations can be written based on one variable or more than one variable. Linear equations consist of constants and variables, and the numbers beside the variables are known as ‘coefficients’. The coefficients and the constants in linear equations can be integers or fractions, and accordingly we can solve the equation to find the value of the variable. The basic method of solving any linear equation always remains the same, however according to the numbers used; the calculations differ in each case.

Example 1: Solve the given linear equation with fractions, x – 2/3 = 5/3 and find the variable of ‘x’.
Given linear equation: x – 2/3 = 5/3
In order to find the value of ‘x’, we first have to get rid of ‘2/3’ on its side.
This implies, add 2/3 on both sides of the equation.
This gives: x – 2/3 + 2/3 = 5/3 + 2/3
So, x = 5/3 + 2/3 ==> x = 7/3.
Therefore the value of the variable ‘x’ in the given equation is 7/3.

Example 2: Solve the given linear equation with fractions, x + 9/4 = 3/4 and find the variable of ‘x’.
Given linear equation: x + 9/4 = 3/4
In order to find the value of ‘x’, we first have to get rid of ‘9/4’ on its side.
This implies, subtract 9/4 on both sides of the equation.
This gives: x + 9/4 – 9/4 = 3/4 - 9/4
So, x = 3/4 - 9/4 ==> x = -6/4
Therefore the value of the variable ‘x’ in the given equation is -6/4.