1-Step Inequalities Worksheet: Practice And Solutions
Table of Contents :
In mathematics, inequalities play a crucial role in understanding and representing relationships between quantities. One of the fundamental types of inequalities is the 1-step inequality, which allows learners to develop their problem-solving skills. This article will delve into the concept of 1-step inequalities, provide a worksheet for practice, and offer solutions to enhance your learning experience. Let's dive in! 📚
Understanding 1-Step Inequalities
A 1-step inequality involves an unknown variable, typically denoted as (x), which is compared to a number using inequality symbols such as:
- (<) (less than)
- (>) (greater than)
- (\leq) (less than or equal to)
- (\geq) (greater than or equal to)
Example:
The inequality (x + 3 < 7) can be solved to find the value of (x).
Solving 1-Step Inequalities
To solve a 1-step inequality, follow these basic steps:
- Isolate the variable: Use the inverse operation to move the constant from one side of the inequality to the other.
- Reverse the inequality sign: If you multiply or divide both sides of the inequality by a negative number, remember to flip the inequality sign.
- Write the solution: Express the solution in terms of the variable (x) and make sure to provide it in interval notation if necessary.
Example Solutions
Here are a few examples to illustrate how to solve 1-step inequalities:
-
Solve (x + 5 > 10)
[ x > 10 - 5 \implies x > 5 ] -
Solve (-2x \leq 6)
[ x \geq \frac{6}{-2} \implies x \geq -3 \quad (\text{flip the sign because of division by a negative}) ]
1-Step Inequalities Worksheet
Now that we understand how to solve 1-step inequalities, let's practice with a worksheet. Below are some problems for you to solve.
Practice Problems
| Problem | Solve the Inequality |
|---|---|
| 1. (x - 4 < 2) | |
| 2. (3x \geq 9) | |
| 3. (x + 10 > 15) | |
| 4. (-x < 6) | |
| 5. (2x + 2 \leq 8) |
Important Note: Make sure to show your work for each problem to reinforce your understanding! ✍️
Solutions to the Worksheet
Let’s go through the solutions for each of the practice problems.
Solutions
-
For (x - 4 < 2)
[ x < 2 + 4 \implies x < 6 ] -
For (3x \geq 9)
[ x \geq \frac{9}{3} \implies x \geq 3 ] -
For (x + 10 > 15)
[ x > 15 - 10 \implies x > 5 ] -
For (-x < 6)
[ x > -6 \quad (\text{flip the sign}) ] -
For (2x + 2 \leq 8)
[ 2x \leq 8 - 2 \implies 2x \leq 6 \implies x \leq 3 ]
Summary of Solutions
<table> <tr> <th>Problem</th> <th>Solution</th> </tr> <tr> <td>1. (x - 4 < 2)</td> <td>(x < 6)</td> </tr> <tr> <td>2. (3x \geq 9)</td> <td>(x \geq 3)</td> </tr> <tr> <td>3. (x + 10 > 15)</td> <td>(x > 5)</td> </tr> <tr> <td>4. (-x < 6)</td> <td>(x > -6)</td> </tr> <tr> <td>5. (2x + 2 \leq 8)</td> <td>(x \leq 3)</td> </tr> </table>
Further Learning Resources
To strengthen your understanding of 1-step inequalities and prepare you for more complex inequalities, consider exploring additional resources:
- Online tutorials or videos on solving inequalities
- Math apps or software that provide interactive inequality problems
- Study groups or tutoring sessions with peers to discuss and solve inequalities together
Important Note: "Consistent practice is the key to mastering inequalities." Regularly tackling different types of problems will enhance your skills and confidence in solving mathematical inequalities.
By incorporating these strategies and engaging with practice worksheets, you'll be well-equipped to tackle 1-step inequalities with ease. Happy learning! 🌟