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Solving One-Step Equations

Using inverse operations to solve equations

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Solving One-Step Equations

What is an Equation?

An equation is a statement that two expressions are equal.

Example: x+5=12x + 5 = 12

Inverse Operations

Operations that "undo" each other:

  • Addition ↔ Subtraction
  • Multiplication ↔ Division

Solving Addition Equations

Undo addition with subtraction

x+5=12x + 5 = 12 x+5−5=12−5x + 5 - 5 = 12 - 5 x=7x = 7

Solving Subtraction Equations

Undo subtraction with addition

x−3=10x - 3 = 10 x−3+3=10+3x - 3 + 3 = 10 + 3 x=13x = 13

Solving Multiplication Equations

Undo multiplication with division

4x=204x = 20 4x4=204\frac{4x}{4} = \frac{20}{4} x=5x = 5

Solving Division Equations

Undo division with multiplication

x3=7\frac{x}{3} = 7 3×x3=7×33 \times \frac{x}{3} = 7 \times 3 x=21x = 21

Golden Rule

Whatever you do to one side, do to the other side!

This keeps the equation balanced.

Checking Solutions

Substitute your answer back into the original equation.

If both sides are equal, you're correct!

📚 Practice Problems

1Problem 1easy

❓ Question:

Solve: x+8=15x + 8 = 15

💡 Show Solution

Subtract 8 from both sides:

x+8−8=15−8x + 8 - 8 = 15 - 8

x=7x = 7

Check: 7+8=157 + 8 = 15 ✓

Answer: x=7x = 7

2Problem 2medium

❓ Question:

Solve: 6x=426x = 42

💡 Show Solution

Divide both sides by 6:

6x6=426\frac{6x}{6} = \frac{42}{6}

x=7x = 7

Check: 6(7)=426(7) = 42 ✓

Answer: x=7x = 7

3Problem 3hard

❓ Question:

Solve: x−5=9\frac{x}{-5} = 9

💡 Show Solution

Multiply both sides by −5-5:

−5×x−5=9×(−5)-5 \times \frac{x}{-5} = 9 \times (-5)

x=−45x = -45

Check: −45−5=9\frac{-45}{-5} = 9 ✓

Answer: x=−45x = -45

4Problem 4medium

❓ Question:

Solve: x/5 = 8

💡 Show Solution

Step 1: Identify the operation. x is being divided by 5

Step 2: Use inverse operation (multiply by 5). Multiply both sides by 5: 5 × (x/5) = 5 × 8

Step 3: Simplify. x = 40

Step 4: Check. 40/5 = 8 ✓

Answer: x = 40

5Problem 5hard

❓ Question:

You have some money. After spending 15,youhave15, you have 42 left. Write and solve an equation to find how much money you started with.

💡 Show Solution

Step 1: Define the variable. Let x = money you started with

Step 2: Write the equation. Starting money - spent = left x - 15 = 42

Step 3: Solve (add 15 to both sides). x - 15 + 15 = 42 + 15 x = 57

Step 4: Check. 57−57 - 15 = $42 ✓

Step 5: Answer the question. You started with $57

Answer: x = 57; You started with $57

Explain using:

⚠️ Common Mistakes: Solving One-Step Equations

Avoid these 3 frequent errors

🌍 Real-World Applications: Solving One-Step Equations

See how this math is used in the real world

📝 Worked Example: Solving a Quadratic by Factoring

Problem:

Solve x2−5x+6=0x^2 - 5x + 6 = 0.

2Factor the quadratic
3Set each factor equal to zero
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📌 Related Topics in Introduction to Algebra

Variables and ExpressionsCombining Like TermsDistributive PropertySolving Two-Step Equations

❓ Frequently Asked Questions

What is Solving One-Step Equations?▾
Using inverse operations to solve equations
How can I study Solving One-Step Equations effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 5 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Solving One-Step Equations study guide free?▾
Yes — all study notes, flashcards, and practice problems for Solving One-Step Equations on Study Mondo are free to access. No account is needed.
What course covers Solving One-Step Equations?▾
Solving One-Step Equations is part of the Pre-Algebra course on Study Mondo, specifically in the Introduction to Algebra section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Solving One-Step Equations?▾
Yes, this page includes 5 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.