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Solving One and Two-Step Equations

Solve equations using inverse operations and check solutions.

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Solving One and Two-Step Equations

One-Step Equations

Use inverse operations to isolate the variable:

x+7=12  ⟹  x=12−7=5x + 7 = 12 \implies x = 12 - 7 = 5 x−3=9  ⟹  x=9+3=12x - 3 = 9 \implies x = 9 + 3 = 12 4x=28  ⟹  x=28÷4=74x = 28 \implies x = 28 \div 4 = 7 x5=6  ⟹  x=6×5=30\frac{x}{5} = 6 \implies x = 6 \times 5 = 30

Two-Step Equations

Undo addition/subtraction first, then multiplication/division:

2x+5=132x + 5 = 13 2x=82x = 8 x=4x = 4

x3−4=2\frac{x}{3} - 4 = 2 x3=6\frac{x}{3} = 6 x=18x = 18

Equations with Negative Numbers

−3x+9=0-3x + 9 = 0 −3x=−9-3x = -9 x=3x = 3

Checking Your Solution

Always substitute back: If x=4x = 4 in 2x+5=132x + 5 = 13: 2(4)+5=8+5=132(4) + 5 = 8 + 5 = 13 ✓

Writing Equations from Words

WordsEquation
"5 more than a number is 12"n+5=12n + 5 = 12
"A number divided by 3 equals 7"n3=7\frac{n}{3} = 7
"Twice a number minus 4 is 10"2n−4=102n - 4 = 10

Golden rule: Whatever you do to one side, do to the other. Keep the equation balanced!

Explain using:

⚠️ Common Mistakes: Solving One and Two-Step Equations

Avoid these 3 frequent errors

🌍 Real-World Applications: Solving One and Two-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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Solving and Graphing Inequalities
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📌 Related Topics in Equations and Inequalities

Solving and Graphing Inequalities

❓ Frequently Asked Questions

What is Solving One and Two-Step Equations?▾
Solve equations using inverse operations and check solutions.
How can I study Solving One and Two-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. Regular review and active practice are key to retention.
Is this Solving One and Two-Step Equations study guide free?▾
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What course covers Solving One and Two-Step Equations?▾
Solving One and Two-Step Equations is part of the Pre-Algebra course on Study Mondo, specifically in the Equations and Inequalities section. You can explore the full course for more related topics and practice resources.