Algebraic equation is a representation of descriptive objective involving some numeric values with symbols. Equation contains two sides with an equality operator “=” such that the contents in the left side of the operator equals the contents in the right side of the operator. The descriptive objective is denoted with some constants,  variables and mathematical operator such as “+”, “-“, “×” etc. Linear means the highest power of any variable is one. For example, in the equation x + 7 = 10, the power of x is 1. So it is a linear equation.

Example: An online agency pays $2 for submitting each micro task and a bonus which is equal to the number of microtasks. If you earn $60, how many microtasks have you submitted?

It is a common practice to denote the unknown with some variable. Let x be the number of micro tasks submitted. Since $2 is paid for submitting 1 microtask, the dollar amount for submitting x microtasks will be 2x. Also a bonus is paid which is equal to the number of microtasks, which is x in this case. So the total amount you should earn,

2x + x

Now this should equal to $60. So, we can write in equation form as below

2x + x = 60 \\

or, 3x = 60 \\

or, \frac{3x}{3} = \frac{60}{3} \footnotesize\text { divide with 3 on both sides} \\

or, x = 20 \\

So, you have submitted 20 microtask

Some rules about equation:

• Any operation (such as addition, subtraction, multiplication or division) in addition to the given objective, performed on equation should be done on both sides of the equation.

Let  x + 7 = 10 be the given objective. If we want to add 3 to the equation, we have to add it in both sides so that the equation satisfies the condition

      x + 7 + 3 = 10 +3 \\

• If we want to change the variables or constant from one side of the equation to other side, we need to change its sign as ‘+’ to ‘-‘ and ‘-‘ to ‘+’

Let given equation be 3x + 20 = x + 60 \\

It can be written as,

3x – x = 60 – 20  \footnotesize\text { changing sides of variables and constants} \\

or,   2x = 40 \\

or, x = 20 \footnotesize\text { divide by 2 on both sides}

Example:

\text { Solve for} x: 17x – 30 = -3x + 110

The above equation can be written as,

17x + 3x = 110 + 30

or, 20x = 140

or, x = 7

Example:

\text {Solve for} x: \frac{x+3}{5} + \frac{2x-7}{3} = \frac{x}{2}

To solve this type of fractional equation, we need to multiply both sides of the equation with least common multiple of 5, 3 and 2 which is 30. The equation can be written as,

30\times\frac{x+3}{5} + 30\times\frac{2x-7}{3} = 30\times\frac{x}{2} \\

or, 6(x+3) + 10(2x-7) = 15x

or, 6x + 18 + 20x - 70 = 15x

or, 6x + 20x - 15x = 70 - 18

or, 11x = 52

or, x = \frac{52}{11}