Two-Step Equations Worksheet With Answers - Practice Made Easy
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Two-step equations are an essential component of algebra that help students develop their problem-solving skills. They provide a foundation for understanding more complex mathematical concepts. In this article, we will explore what two-step equations are, how to solve them, and provide a worksheet with answers to make your practice easy and effective!
What Are Two-Step Equations?
Two-step equations are equations that can be solved in two steps. Generally, they take the form:
[ ax + b = c ]
Where:
- ( a ) is a coefficient (a number multiplied by the variable)
- ( x ) is the variable (the unknown we are trying to solve for)
- ( b ) is a constant (a number that does not change)
- ( c ) is another constant
The goal is to isolate ( x ) on one side of the equation.
How to Solve Two-Step Equations
To solve a two-step equation, follow these simple steps:
-
Isolate the variable term: This involves getting rid of the constant on the same side as the variable. You can do this by subtracting or adding that constant from both sides of the equation.
-
Solve for the variable: Once you have isolated the variable term, divide or multiply to find the value of the variable.
Here’s a quick example:
Example
Let's solve the equation:
[ 3x + 4 = 19 ]
Step 1: Subtract 4 from both sides:
[ 3x + 4 - 4 = 19 - 4 ]
This simplifies to:
[ 3x = 15 ]
Step 2: Divide both sides by 3:
[ x = \frac{15}{3} ]
Therefore,
[ x = 5 ]
Two-Step Equation Worksheet
Now that you understand how to solve two-step equations, let’s put your skills to the test with a worksheet! Below are some practice problems along with a table for answers.
Practice Problems
Solve the following equations:
- ( 5x - 3 = 22 )
- ( 2x + 6 = 20 )
- ( 4x - 7 = 9 )
- ( 3x + 5 = 20 )
- ( 6x - 1 = 17 )
- ( 8x + 3 = 43 )
- ( 9x - 5 = 22 )
- ( 2x + 10 = 34 )
- ( 7x - 4 = 24 )
- ( 3x + 8 = 23 )
Answers
Here are the solutions to the above problems in a table format:
<table> <tr> <th>Equation</th> <th>Solution</th> </tr> <tr> <td>1. ( 5x - 3 = 22 )</td> <td> ( x = 5 )</td> </tr> <tr> <td>2. ( 2x + 6 = 20 )</td> <td> ( x = 7 )</td> </tr> <tr> <td>3. ( 4x - 7 = 9 )</td> <td> ( x = 4 )</td> </tr> <tr> <td>4. ( 3x + 5 = 20 )</td> <td> ( x = 5 )</td> </tr> <tr> <td>5. ( 6x - 1 = 17 )</td> <td> ( x = 3 )</td> </tr> <tr> <td>6. ( 8x + 3 = 43 )</td> <td> ( x = 5 )</td> </tr> <tr> <td>7. ( 9x - 5 = 22 )</td> <td> ( x = 3 )</td> </tr> <tr> <td>8. ( 2x + 10 = 34 )</td> <td> ( x = 12 )</td> </tr> <tr> <td>9. ( 7x - 4 = 24 )</td> <td> ( x = 4 )</td> </tr> <tr> <td>10. ( 3x + 8 = 23 )</td> <td> ( x = 5 )</td> </tr> </table>
Important Notes
- Remember, the key to mastering two-step equations is practice!
- Always check your work by plugging the value of ( x ) back into the original equation to ensure that both sides are equal.
- Use the worksheet to identify areas where you might need additional practice or clarification.
Conclusion
Two-step equations are a foundational skill in algebra that sets the stage for more advanced mathematical concepts. By practicing regularly with worksheets and checking your understanding, you can gain confidence and proficiency in solving these equations. Don't hesitate to revisit the steps whenever needed, and remember to practice regularly! Happy solving! ✨