# Solving Two step Equations

The transposition rules for solving simple algebraic equations are formed based on the properties of equality.
• If a number is added to a variable or to an expression containing the variable, then subtract the number on the other side.
• If a number is subtracted to a variable or to an expression containing the variable, then add the number on the other side.
• If a variable or an expression containing a variable is multiplied by a number, then divide the expression on the other side by the number.
• If a variable or an expression containing a variable is divided by a number, then divide the expression on the other side by the number.
Definition - Two step equations
An equation which is solved using transposition rules is known an two-step equations.
When an equation is solved in two steps, any one of the given combination of the above given rules is applied.
• Transposition of Multiplication and Addition.
• Transposition of Multiplication and subtraction
• Transposition of Division and Addition
• Transposition of Division and subtraction
Note: The combination will not include two inverse operations, like addition with subtraction or multiplication with division.

## Two Step Equations

An equation in x is a statement that two algebraic expressions are equal. To solve an equation in x means to find all values of x for which the equation is true. A linear equation in one variable x is an equation that can written in the slandered form, ax + b = 0, where a and b are real numbers, with a $\neq$ 0. Two step equations is the way to find the solution for the linear equations in two steps.

### Solved Example

Question: Solve the equation, 3x + 5 = 29
Solution:
The expression on the right side is formed by multiplying the variable by 3 and adding 5 to the product.

Step 1:
Subtract 5 from both sides,

3x + 5 - 5 = 29 - 5

3x = 24

Step 2:
Divide both side by 3

$\frac{3x}{3} = \frac{24}{3}$

=>  x = 8

## How to Solve Two Step Equations

Two step equations are solved as same as one step equations. To perform two steps in order to solve the equation ax + b = c. We need to get rid of the "b"  that is added, so we’ll need to subtract "b" from both sides. Even after doing that, there is still "a" multiplied by the variable, so division will be necessary to eliminate it.

### Solved Examples

Question 1: Solve the equation: 4x - 9 = 31

Solution:
The expression on the left side is formed by multiplying the variable by 4 and subtracting 9 from the product.

Step 1:  Add 9 from both sides of the equation,

4x - 9 + 9 = 31 + 9

4x = 40

Step 2:  Divide both side by 4

$\frac{4x}{4} = \frac{40}{4}$

x = 10 is the answer.

Question 2: Solve the equation

$\frac{P}{4}$ + 8 = 7

Solution:
The expression on the left side is formed by, P is first divided by 4 and then 8 is added to the quotient.

Step 1:
Subtract 8 from both side

$\frac{P}{4}$  + 8 - 8 = 7 - 8

=> $\frac{P}{4}$ = -1

Step 2:
Multiply both side by 4

=> $\frac{P}{4}\times$ 4 = -1 x 4

=> P = - 4, is the answer.

Question 3: Solve the equation

$\frac{n - 5}{2}$ = 5

Solution:
The expression on the left side is formed by subtracted 5 from the variable and then the difference is divided by 2

Step 1: Multiply both side by 2

$\frac{n - 5}{2}$ x 2 = 5 x 2

=>  n - 5 = 10

Step 2: Add 5 from both sides of the equation

n - 5 + 5 = 10 + 5

=> n = 15.