Algebra II involves solving linear equations. Linear equation with one variable is the simplest form of equation. The equations involving only linear polynomials we call as linear equations. The highest power of the variable appearing in linear equation is 1. Any value of the variable which when substituted in an equation makes its both sides equal is called a solution of the equation. To solve an equation we need to follow two permissible rules.
Addition – Subtraction Rule
If any number is added or subtracted from both sides of an equation, the resulting equation has the same solution as the original.
Multiplication – Division Rule
If each side of equation is multiplied or divided by non-zero number, the resulting equation has the same solution as the original.
This can be easily understood by taking the separate examples for using the rules
Example 1:- Find the solution of x – 15 + 7 = 25
Use Addition – Subtraction Rule
To eliminate – 15, add 15 on both sides
x – 15 + 15 + 7= 25 + 15
x + 7= 40
To eliminate + 7, subtract 7 on both sides
x + 7 – 7 = 40 – 7
x = 33
Hence the required solution
This problem helps to understand the Addition – Subtraction rule
Example 2:- Find the solution of 2 x / 3 = 8
Use Multiplication and Division rule.
Multiply by 3 on both sides, 3 in the denominator gets cancelled
3 X 2x/3 = 8 X 3
2x = 24
Divide by 2 on both sides
X= 12; Solution obtained
These examples we applied basic rules for solving linear equation with one variable.