An equation with an unknown number is a mathematical statement where two expressions are set equal to each other, and one or more values are missing. The unknown is usually represented by a letter (like *x*) or a blank space (___). The goal is to find the missing number that makes the equation true.

Examples:

• x+5=8x+5=8
• 12−___=712−___=7
• 3×y=153×y=15
• 20÷x=420÷x=4

Structure of an Equation

An equation always has:

1. Left Side (Expression)
2. Equal Sign (=)
3. Right Side (Expression)

Example: x+3=10x+3=10

Here, x+3x+3 is the left side, and 1010 is the right side. The unknown xx must be found so that both sides are equal.

How to Solve Simple Equations

1. Addition Equations

Example: x+4=7x+4=7

• Question: What number added to 4 gives 7?
• Solution: Subtract 4 from both sides.x+4−4=7−4x+4−4=7−4x=3x=3
• Check: 3+4=73+4=7 ✅

2. Subtraction Equations

Example: 9−x=59−x=5

• Question: What number subtracted from 9 gives 5?
• Solution: Subtract 5 from 9.9−5=x9−5=xx=4x=4
• Check: 9−4=59−4=5 ✅

Alternative Form: x−2=6x−2=6

• Solution: Add 2 to both sides.x−2+2=6+2x−2+2=6+2x=8x=8

3. Multiplication Equations

Example: x×3=12x×3=12

• Question: What number multiplied by 3 equals 12?
• Solution: Divide both sides by 3.x×33=1233x×3​=312​x=4x=4
• Check: 4×3=124×3=12 ✅

4. Division Equations

Example: 20÷x=420÷x=4

• Question: What number divides 20 to give 4?
• Solution: Rearrange the equation.20÷x=420÷x=420=4×x20=4×xx=204x=420​x=5x=5
• Check: 20÷5=420÷5=4 ✅

Alternative Form: x2=82x​=8

• Solution: Multiply both sides by 2.x=8×2x=8×2x=16x=16

Examples:

Example 1:

• Equation: x+6=10.
• Solution: To find the missing number, think about what number you add to 6 to make 10. The answer is 4.
• Complete Equation: 4+6=10.

Example 2:

• Equation: 8-x=3
• Solution: To find the missing number, think about what number you subtract from 8 to get 3. The answer is 5.
• Complete Equation: 8−5=3.

Example 3:

• Equation: x+7=12.
• Solution: To find the missing number, think about what number you add to 7 to make 12. The answer is 5.
• Complete Equation: 5+7=12.

Example 4:

• Equation: x×4=20\_ \times 4 = 20_×4=20
• Solution: To find the missing number, think about what number multiplied by 4 equals 20. The answer is 5.
• Complete Equation: 5×4=20

Example 5:

• Equation: 6×x=30
• Solution: To find the missing number, think about what number multiplied by 6 equals 30. The answer is 5.
• Complete Equation: 6×5=30.

Example 6:

• Equation: 18÷x=6
• Solution: To find the missing number, think about what number divides 18 to give 6. The answer is 3.
• Complete Equation: 18÷3=6

Example 7:

• Equation: x÷4=5
• Solution: To find the missing number, think about what number divided by 4 equals 5. The answer is 20.
• Complete Equation: 20÷4=5