Solve For { X $} . . . { 15 = \frac{x}{-2} + 7 \}
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Introduction
Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving linear equations with one variable, specifically the equation 15 = x/-2 + 7. We will break down the solution process into manageable steps, making it easy for readers to understand and apply.
Understanding the Equation
Before we dive into the solution, let's take a closer look at the equation 15 = x/-2 + 7. This equation is a linear equation with one variable, x. The equation is in the form of ax + b = c, where a, b, and c are constants.
- a is the coefficient of the variable x, which is -2 in this case.
- b is the constant term on the right-hand side of the equation, which is 7.
- c is the constant term on the left-hand side of the equation, which is 15.
Step 1: Isolate the Variable
To solve for x, we need to isolate the variable on one side of the equation. In this case, we can start by subtracting 7 from both sides of the equation.
15 = x/-2 + 7
15 - 7 = x/-2 + 7 - 7
8 = x/-2
Step 2: Eliminate the Fraction
Now that we have the equation 8 = x/-2, we can eliminate the fraction by multiplying both sides of the equation by -2.
8 = x/-2
8 * -2 = x/-2 * -2
-16 = x
Step 3: Solve for x
Finally, we have isolated the variable x on one side of the equation. We can now solve for x by multiplying both sides of the equation by 1 (since any number multiplied by 1 is itself).
-16 = x
x = -16
Conclusion
In this article, we have solved the linear equation 15 = x/-2 + 7 using a step-by-step approach. We started by isolating the variable x, then eliminated the fraction, and finally solved for x. By following these steps, readers can confidently solve linear equations with one variable.
Tips and Tricks
- Check your work: Always check your solution by plugging it back into the original equation.
- Use a calculator: If you're struggling to solve an equation, try using a calculator to check your work.
- Practice, practice, practice: The more you practice solving linear equations, the more confident you'll become.
Common Mistakes
- Forgetting to isolate the variable: Make sure to isolate the variable on one side of the equation before solving for it.
- Not eliminating the fraction: Don't forget to eliminate the fraction by multiplying both sides of the equation by the denominator.
- Not checking your work: Always check your solution by plugging it back into the original equation.
Real-World Applications
Linear equations have many real-world applications, including:
- Physics: Linear equations are used to describe the motion of objects under constant acceleration.
- Engineering: Linear equations are used to design and optimize systems, such as electrical circuits and mechanical systems.
- Economics: Linear equations are used to model economic systems and make predictions about future trends.
Final Thoughts
Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, readers can confidently solve linear equations with one variable. Remember to check your work, use a calculator, and practice, practice, practice. With time and practice, you'll become a pro at solving linear equations.
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Introduction
In our previous article, we covered the basics of solving linear equations with one variable. However, we know that practice makes perfect, and sometimes, it's helpful to have a Q&A guide to clarify any doubts. In this article, we'll address some common questions and provide step-by-step solutions to help you master the art of solving linear equations.
Q1: What is a linear equation?
A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it's an equation that can be written in the form ax + b = c, where a, b, and c are constants.
Q2: How do I solve a linear equation with one variable?
To solve a linear equation with one variable, follow these steps:
- Isolate the variable: Get the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
- Eliminate the fraction: If the equation has a fraction, multiply both sides of the equation by the denominator to eliminate the fraction.
- Solve for the variable: Once the variable is isolated, solve for it by performing the necessary operations.
Q3: What is the difference between a linear equation and a quadratic equation?
A linear equation is an equation in which the highest power of the variable(s) is 1, whereas a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example:
- Linear equation: 2x + 3 = 5
- Quadratic equation: x^2 + 4x + 4 = 0
Q4: How do I solve a linear equation with a fraction?
To solve a linear equation with a fraction, follow these steps:
- Eliminate the fraction: Multiply both sides of the equation by the denominator to eliminate the fraction.
- Isolate the variable: Get the variable on one side of the equation by adding, subtracting, multiplying, or dividing both sides of the equation by the same value.
- Solve for the variable: Once the variable is isolated, solve for it by performing the necessary operations.
Q5: What is the order of operations when solving a linear equation?
When solving a linear equation, follow the order of operations (PEMDAS):
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q6: How do I check my solution to a linear equation?
To check your solution to a linear equation, plug the solution back into the original equation and verify that it's true. If the solution satisfies the equation, then it's correct.
Q7: What are some common mistakes to avoid when solving linear equations?
Some common mistakes to avoid when solving linear equations include:
- Forgetting to isolate the variable: Make sure to isolate the variable on one side of the equation before solving for it.
- Not eliminating the fraction: Don't forget to eliminate the fraction by multiplying both sides of the equation by the denominator.
- Not checking your work: Always check your solution by plugging it back into the original equation.
Q8: How can I practice solving linear equations?
To practice solving linear equations, try the following:
- Work through practice problems: Use a textbook or online resource to find practice problems to work through.
- Use a calculator: If you're struggling to solve an equation, try using a calculator to check your work.
- Join a study group: Join a study group or find a study buddy to practice solving linear equations together.
Conclusion
Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and practicing regularly, you'll become confident in your ability to solve linear equations. Remember to check your work, use a calculator, and practice, practice, practice. With time and practice, you'll become a pro at solving linear equations.