One Variable Equations

Grade 6 · algebra · 96 practice problems · read aloud

🔊 Listen to this explanation

One-Variable Equations: Finding the Missing Number

🔍 What is it and Why is it Useful?

An equation is like a balanced scale. Both sides are equal. A one-variable equation has one unknown number, often represented by a letter like x or n. We solve it to find the value of that missing number. This is super useful for solving real-life puzzles, like figuring out how many points you need on a test to get an A, or how many weeks you need to save your allowance to buy a new game.

📝 Step-by-Step Guide to Solving

  1. Identify the Goal: Find the value of the variable (e.g., x).
  2. Isolate the Variable: Use inverse operations to get the variable by itself on one side of the equals sign.
  3. Keep it Balanced: Whatever you do to one side of the equation, you MUST do to the other side.
  4. Check Your Answer: Plug your solution back into the original equation to see if it makes a true statement.

✨ Visual Examples

Example 1: x + 7 = 15

  1. The inverse of +7 is -7. Subtract 7 from both sides.
  2. x + 7 - 7 = 15 - 7
  3. Simplify: x = 8 ✅
  4. Check: 8 + 7 = 15 ✔️

Example 2: 3y = 21

  1. The inverse of multiplying by 3 is dividing by 3. Divide both sides by 3.
  2. 3y ÷ 3 = 21 ÷ 3
  3. Simplify: y = 7 ✅
  4. Check: 3 × 7 = 21 ✔️

⚠️ Common Mistakes to Avoid

  • Forgetting to Balance: Only performing an operation on one side. Remember, the scale must stay balanced!
  • Incorrect Inverse Operations: Mixing up addition/subtraction with multiplication/division.
  • Skipping the Check: Always verify your answer to catch simple calculation errors.

💡 Tips & Tricks

  • Think of the equation as a balance scale—it's a perfect visual!
  • Undo the operations around the variable in the reverse order of PEMDAS (SADMEP).
  • Draw arrows showing what you're doing to both sides to help you remember to keep it balanced.

🎯 How to Practice

Start simple and build your skills!

  • Create your own equations and solve them.
  • Use online practice websites like Khan Academy or IXL for instant feedback.
  • Turn word problems into equations. For example: "I have 12 cookies after eating 3. How many did I start with?" becomes x - 3 = 12.

Practice problems

6 of the 96, worked through step by step — try them before opening the answer.

1 3x + 15 = 42

Hint: Isolate the variable by performing inverse operations on both sides of the equation.

Show the answer

Answer: 9

  1. Subtract 15 from both sides of the equation. Reason: We want to isolate the term with the variable (3x). Calculation: 3x + 15 - 15 = 42 - 15 3x = 27
  2. Divide both sides by 3. Reason: To solve for x, we need to remove the coefficient 3 from x. Calculation: 3x / 3 = 27 / 3 x = 9 Final answer: x = 9.

We are solving the equation: 3x + 15 = 42.

2 3x + 15 = 36

Hint: Isolate the variable by performing inverse operations on both sides of the equation.

Show the answer

Answer: 7

  1. Subtract 15 from both sides of the equation. Reason: We want to isolate the term with the variable (3x) on one side. Since 15 is added to 3x, we do the opposite operation (subtraction) to both sides to remove it from the left side. Calculation: 3x + 15 - 15 = 36 - 15 This simplifies to: 3x = 21
  2. Divide both sides by 3. Reason: The variable x is multiplied by 3. To solve for x, we do the opposite operation (division) to both sides. Calculation: 3x / 3 = 21 / 3 This simplifies to: x = 7 Final answer: x = 7

We are solving the equation: 3x + 15 = 36.

3 x + 2048 = 5000

Hint: Think about what operation you need to perform to isolate the variable x. Look at the number being added to x and consider its opposite.

Show the answer

Answer: 2952

  1. The equation is x + 2048 = 5000.
  2. To isolate x, subtract 2048 from both sides of the equation.
  3. x + 2048 - 2048 = 5000 - 2048
  4. Simplify: x = 2952
  5. Check: 2952 + 2048 = 5000, which is correct.

The answer is 2952.

4 x + 1357 = 2846

Hint: Think about what operation you need to use to undo the addition and get x by itself.

Show the answer

Answer: 1489

  1. Start with the equation x + 1357 = 2846.
  2. To isolate x, subtract 1357 from both sides of the equation.
  3. x + 1357 - 1357 = 2846 - 1357
  4. Simplify: x = 1489
  5. Check: 1489 + 1357 = 2846.

The answer is 1489.

5 x + 1272 = 2847

Hint: Think about what operation you need to perform to isolate x. The equation shows x plus a number equals another number.

Show the answer

Answer: 1575

  1. The equation is x + 1272 = 2847.
  2. To isolate x, subtract 1272 from both sides of the equation.
  3. x + 1272 - 1272 = 2847 - 1272
  4. Simplify: x = 1575
  5. Check: 1575 + 1272 = 2847 ✓

The answer is 1575.

6 x + 2847 = 5000

Hint: Think about what operation you need to perform to isolate x. The equation shows addition, so you can use the inverse operation to find the value of x.

Show the answer

Answer: 2153

  1. The equation is x + 2847 = 5000.
  2. To isolate x, subtract 2847 from both sides of the equation.
  3. x + 2847 - 2847 = 5000 - 2847
  4. Simplify: x = 2153
  5. Check: 2153 + 2847 = 5000. Correct.

The answer is 2153.

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