A simple equation is a mathematical statement that shows that two expressions are equal, containing an unknown value (usually represented by a letter such as x, y, or n). Solving a simple equation means finding the value of the unknown that makes the equation true.

• Unknown: The letter representing the value to be found.


• Coefficient: The number multiplying the unknown.


• Constant: A fixed number in the equation.


• Equality Sign (=): Shows that both sides of the equation are equal.

Example:

3x + 5 = 20

Unknown: x

Coefficient: 3

Constant: 5

Equality sign: =

Steps to Solve Simple Equations

1. Identify the unknown.


2. Use inverse operations to isolate the unknown:
   
   
   • If there is addition, subtract it from both sides.
   
   
   • If there is subtraction, add it to both sides.
   
   
   • If the unknown is multiplied, divide both sides by the coefficient.
   
   
   • If the unknown is divided, multiply both sides by the denominator.
   
   
3. Check the solution by substituting it back into the original equation.

Worked Examples

Example 1: Solve 2x + 5 = 15

Step 1: Subtract 5 from both sides: 2x = 10

Step 2: Divide by 2: x = 5

Check: 2 × 5 + 5 = 10 + 5 = 15

Example 2: Solve x - 7 = 8

Step 1: Add 7 to both sides: x = 15

Check: 15 - 7 = 8

Example 3: Solve 4x = 20

Step 1: Divide both sides by 4: x = 5

Check: 4 × 5 = 20

Example 4: Solve 18 ÷ x = 6

Step 1: Multiply both sides by x: 18 = 6x

Step 2: Divide both sides by 6: x = 3

Check: 18 ÷ 3 = 6

Example 5: Solve 3x - 4 = 11

Step 1: Add 4 to both sides: 3x = 15

Step 2: Divide by 3: x = 5

Check: 3 × 5 - 4 = 15 - 4 = 11

Example 6: Solve 5 + x = 12

Step 1: Subtract 5 from both sides: x = 7

Check: 5 + 7 = 12

Important Notes

• Always perform the same operation on both sides of the equation.


• Check your solution by substituting it back into the original equation.


• Simple equations can involve addition, subtraction, multiplication, or division, but only one unknown at a time.