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Z.2 Solve equations with an unknown

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What is an unknown in an equation?

An unknown is a missing number in an equation. It is often shown with a letter or a blank space. Your job is to figure out what number makes the equation true.

Examples:
  • 7 + [] = 15
  • x − 4 = 9
  • 3 × n = 18
Note

The unknown is like a puzzle piece. When you find the correct number, both sides of the equation match.

Solving addition equations with an unknown

To solve an addition equation with an unknown, think about what number must be added to reach the total.

Example:
  • 8 + x = 14
  • Ask: “What number plus 8 equals 14?” → x = 6
Note

You can subtract the known number from the total to find the missing number.

Solving subtraction equations with an unknown

To solve a subtraction equation with an unknown, decide whether the unknown is the number being subtracted or the starting number.

Examples:
  • a − 5 = 12 → a = 17
  • 20 − b = 8 → b = 12
Note

If the unknown is at the beginning, add to find it. If the unknown is being subtracted, subtract to find it.

Solving multiplication equations with an unknown

To solve a multiplication equation with an unknown, think about what number multiplied by the known number gives the product.

Example:
  • 3 × m = 21
  • Ask: “3 times what equals 21?” → m = 7
Note

You can divide the product by the known number to find the unknown.

Solving division equations with an unknown

To solve a division equation with an unknown, decide whether the unknown is the number being divided or the divisor.

Examples:
  • k ÷ 4 = 3 → k = 12
  • 30 ÷ d = 5 → d = 6
Note

Use multiplication to help check your answer. If the multiplication works, the solution is correct.

Using the inverse relationship of operations

Inverse operations are pairs of operations that undo each other. Addition and subtraction are inverses, and multiplication and division are inverses.

Examples:
  • If 9 + x = 20, use subtraction: 20 − 9 = x → x = 11
  • If 5 × p = 40, use division: 40 ÷ 5 = p → p = 8
Note

Using inverse operations helps you check your work and understand how equations are connected.

Checking your solution

After solving an equation, replace the unknown with your answer to see if both sides are equal.

Example:
  • 7 + q = 19 → q = 12
  • Check: 7 + 12 = 19 ✓
Note

If both sides match, your answer is correct. If not, solve again using a different strategy.