Solve Inequalities With Fractions

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Inequality is the equation which has less than or greater than symbols in it i.e. '<' and '>' respectively. Equality is when we can equate both sides of the equation and is represented by ‘=’. Fraction is usually written in the “p/q” form. Here ‘p’ is the numerator and 'q' is the denominator. The denominator of a fraction cannot be equal to zero i.e. q not equal to zero. Fraction are very commonly used and very important form of representation of numbers. Some fractions can be further simplified according to the requirement. Different mathematical operations can be used to simplify and solve a given fraction.

Example 1: Solve the inequality 2x – 2/5 > 3/5?

Solution: Given equation is 2x – 2/5 > 3/5.
Here the unknown variable which needs to be solved for is x.
Step 1: Add 2/5 on both sides of the equation.
This gives 2 x -2/5 + 2/5 > 3/5 + 2/5; 2x > 5/5; 2x > 1
Divide both sides of the equation by 2; 2x/2 > 1/2
Hence the solution is x > 1/2.
 

Example 2: Solve the inequality 6x – 5/4 > 3/4?

Solution: Given equation is 6x – 5/4 > 3/4.
Here the unknown variable which needs to be solved for is x.
Step 1: Add 5/4 on both sides of the equation.
This gives 6 x -5/4 + 5/4 > 3/4 + 5/4; 6 x > 8 /4; 6 x > 2.
Divide both sides of the equation by 6; 6x/6 > 2/6
Hence the solution is x > 1/3.

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