Equations consist of one or more than one unknown variables (such as: x, y,a,b etc.) with different coefficients and constant numbers. Exponent is the degree of the variable in the equation. The degree of the variable can be one or more than one. Equations are the very common and used in almost every topic in mathematics. There are various mathematical operations which are used to simplify and solve equations.
Example 1: Simplify and solve for y in the equation 7 y – 19 = 51?
Solution: Given equation is 7 y – 19 = 51.
Here the unknown variable which needs to be solved for is y.
First step: Adding 19 on both sides of the given equation.
Therefore, (10 y – 19) + 19 = 51 + 19; 7y = 70.
Now dividing both sided of the equation by 7; this gives 7 y/7 = 70/7.
This reduces the given equation to y = 10.
Hence the solution is y = 10.
Example 2: Simplify the equation and solve for y if x =3
y = 5 (x – 2) + 10?
Solution: Given equation is y = 5 (x – 2) + 10.
Here the variable is x; distributing the number in front of the braces.
This gives 5 (x - 2) = 5 x – 10; this gives y = 5 x - 10 + 10 = 5x.
The equation reduces to y = 5x, given x = 3.
Substituting the value y = 5* 3 = 15
Hence the solution if y = 15.