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Math has many branches and sub branches. Each branch has its own set of problems which can be solved using different mathematical properties, theorems and formulas. Algebra is one of the most important and prominent branches of mathematics. The study of algebra consists of solving for the known and unknown variables. There are different mathematical operations such as addition, subtraction, multiplication and division which can be used to solve the problems according to the requirement.

Example 1: Solve the equation 10(x – 5) + 5(x + 5) at x = 3?

Solution: Given equation is 10 (x – 5) + 5 (x + 5).
Here the variable is x; distributing the number in front of the braces.
This gives 10 (x - 5) = 10 x – 50; 5 (x + 5) = 5 x + 25.
Combining the similar terms in the equation.
This gives 10x – 50 + 5x + 25 = 15 x – 25.
Substitute x = 3; 15(3) – 25 = 20

Hence the solution is 20.
 
Example 2: Simplify and solve for x in the equation 15 x + 5 = 80?

Solution: Given equation is 15 x + 5 = 80.
Here the unknown variable which needs to be solved for is x.
First step: Subtract 5 on both sides of the given equation.
(15 x + 5) - 5 = 80 - 5. This gives 15 x = 75.
Now dividing both sided of the equation by 15.That is 15 x/ 15 = 75 / 15.

Hence the solution is x = 5.


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