The transposition rules for solving simple algebraic equations are formed based on the properties of equality.

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.

- 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.

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

## Two Step Equations

### 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.

3x + 5 - 5 = 29 - 5

3x = 24

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

=> x = 8

**Subtract 5 from both sides,**

Step 1:Step 1:

3x + 5 - 5 = 29 - 5

3x = 24

**Divide both side by 3**

Step 2:Step 2:

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

=> x = 8

## How to Solve Two Step Equations

**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.

4x - 9 + 9 = 31 + 9

4x = 40

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

**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.

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

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

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

=> P = - 4, is the answer.

**Subtract 8 from both side**

Step 1:Step 1:

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

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

**Multiply both side by 4**

Step 2:Step 2:

=> $\frac{P}{4}\times$ 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

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

=> n - 5 = 10

n - 5 + 5 = 10 + 5

=> n = 15.

**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 equationn - 5 + 5 = 10 + 5

=> n = 15.