Solving Multi-Step Equations: A Comprehensive Guide
Solving multi-step equations is a fundamental concept in algebra, and it’s essential to master this skill to succeed in mathematics. In this guide, we’ll provide a step-by-step approach to solving multi-step equations, along with examples and a worksheet answer key.
What are Multi-Step Equations?
Multi-step equations are equations that require more than one step to solve. They involve multiple operations, such as addition, subtraction, multiplication, and division, which must be performed in the correct order to isolate the variable.
Step-by-Step Approach to Solving Multi-Step Equations
To solve multi-step equations, follow these steps:
- Simplify the equation: Combine like terms, and eliminate any parentheses or brackets.
- Add or subtract the same value to both sides: Get rid of any constants or terms on the same side as the variable by adding or subtracting the same value to both sides of the equation.
- Multiply or divide both sides: If the variable is multiplied or divided by a coefficient, multiply or divide both sides of the equation by the same value to isolate the variable.
- Check your solution: Plug your solution back into the original equation to ensure it’s true.
Examples of Solving Multi-Step Equations
Example 1:
2x + 5 = 11
Solution:
- Subtract 5 from both sides: 2x = 11 - 5
- Simplify: 2x = 6
- Divide both sides by 2: x = 6 ÷ 2
- Simplify: x = 3
Example 2:
x - 3 = 7
Solution:
- Add 3 to both sides: x = 7 + 3
- Simplify: x = 10
Worksheet Answer Key
Here’s a worksheet with 10 multi-step equations, along with the answer key:
| Equation | Solution |
|---|---|
| 1. x + 2 = 9 | x = 7 |
| 2. 3x - 2 = 13 | x = 5 |
| 3. 2x + 4 = 16 | x = 6 |
| 4. x - 1 = 8 | x = 9 |
| 5. 4x - 3 = 21 | x = 6 |
| 6. x + 2 = 11 | x = 9 |
| 7. 2x - 5 = 9 | x = 7 |
| 8. x + 1 = 6 | x = 5 |
| 9. 3x + 2 = 17 | x = 5 |
| 10. x - 2 = 10 | x = 12 |
📝 Note: Make sure to check your solutions by plugging them back into the original equation.
Solving multi-step equations requires patience and practice. Remember to follow the step-by-step approach, and don’t be afraid to check your solutions.
By mastering this skill, you’ll be able to tackle more complex algebra problems with confidence.
What is the most important step in solving multi-step equations?
+The most important step is to simplify the equation by combining like terms and eliminating any parentheses or brackets.
How do I know if my solution is correct?
+Plug your solution back into the original equation to ensure it’s true. If it is, then your solution is correct.
Can I use a calculator to solve multi-step equations?
+While calculators can be helpful, it’s essential to understand the step-by-step process to solve multi-step equations. Calculators can be used to check your solutions, but make sure to show your work.
Related Terms:
- Big ideas 12
- 12 Extra Practice Algebra 1
