Solve The Equation For X X X : − 7 + X 2 = − 11 -7+\frac{x}{2}=-11 − 7 + 2 X = − 11

Mar 13, 2025 by ADMIN 86 views

**Solving Linear Equations: A Step-by-Step Guide**

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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 a simple linear equation, $-7+\frac{x}{2}=-11$ , step by step. We will break down the solution into manageable parts, making it easy to understand and follow along.

Understanding the Equation

The given equation is $-7+\frac{x}{2}=-11$ . Our goal is to isolate the variable $x$ and find its value. To do this, we need to get rid of the fraction and the constant term on the left-hand side of the equation.

Step 1: Get Rid of the Fraction

To eliminate the fraction, we can multiply both sides of the equation by the denominator, which is 2. This will get rid of the fraction and make it easier to work with.

-7 + \frac{x}{2} = -11
\implies 2 \times \left(-7 + \frac{x}{2}\right) = 2 \times (-11)
\implies -14 + x = -22

Step 2: Isolate the Variable

Now that we have eliminated the fraction, we can focus on isolating the variable $x$ . To do this, we need to get rid of the constant term on the left-hand side of the equation.

-14 + x = -22
\implies x = -22 + 14
\implies x = -8

Conclusion

In this article, we solved the linear equation $-7+\frac{x}{2}=-11$ step by step. We eliminated the fraction by multiplying both sides of the equation by the denominator, and then isolated the variable $x$ by getting rid of the constant term. The final solution is $x = -8$ .

Tips and Tricks

When solving linear equations, it's essential to follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
To eliminate fractions, multiply both sides of the equation by the denominator.
To isolate the variable, get rid of the constant term on the left-hand side of the equation.

Real-World Applications

Linear equations have numerous real-world applications, including:

Physics: To describe the motion of objects, we use linear equations to model the position, velocity, and acceleration of objects.
Economics: Linear equations are used to model the demand and supply of goods and services.
Computer Science: Linear equations are used in computer graphics to create 3D models and animations.

Common Mistakes

Not following the order of operations (PEMDAS).
Not eliminating fractions before isolating the variable.
Not checking the solution by plugging it back into the original equation.

Practice Problems

Try solving the following linear equations:

$2x + 5 = 11$
$x - 3 = 7$
$\frac{x}{3} + 2 = 5$

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article, you can solve linear equations with ease. Remember to eliminate fractions, isolate the variable, and check your solution by plugging it back into the original equation. With practice, you will become proficient in solving linear equations and be able to apply them to real-world problems.

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Introduction

In our previous article, we covered the basics of solving linear equations. However, we know that practice makes perfect, and there's no better way to learn than by asking questions and getting answers. In this article, we'll provide a Q&A guide to help you better understand how to solve linear equations.

Q: What is a linear equation?

A: 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.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow these steps:

Eliminate any fractions by multiplying both sides of the equation by the denominator.
Isolate the variable by getting rid of the constant term on the left-hand side of the equation.
Check your solution by plugging it back into the original equation.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when solving an equation. The acronym PEMDAS stands for:

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.

Q: How do I eliminate fractions in a linear equation?

A: To eliminate fractions in a linear equation, multiply both sides of the equation by the denominator. For example, if you have the equation 1/2x + 3 = 7, multiply both sides by 2 to get rid of the fraction.

Q: What is the difference between a linear equation and a quadratic equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. For example, the equation 2x + 5 = 11 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

Q: How do I check my solution to a linear equation?

A: To check your solution to a linear equation, plug the solution back into the original equation and see if it's true. For example, if you solve the equation 2x + 5 = 11 and get x = 3, plug x = 3 back into the original equation to see if it's true.

Q: What are some common mistakes to avoid when solving linear equations?

A: Some common mistakes to avoid when solving linear equations include:

Not following the order of operations (PEMDAS).
Not eliminating fractions before isolating the variable.
Not checking the solution by plugging it back into the original equation.

Q: How do I apply linear equations to real-world problems?

A: Linear equations have numerous real-world applications, including:

Physics: To describe the motion of objects, we use linear equations to model the position, velocity, and acceleration of objects.
Economics: Linear equations are used to model the demand and supply of goods and services.
Computer Science: Linear equations are used in computer graphics to create 3D models and animations.

Conclusion

Solving linear equations is a crucial skill for students to master. By following the steps outlined in this article and practicing with real-world examples, you'll become proficient in solving linear equations and be able to apply them to a variety of problems. Remember to eliminate fractions, isolate the variable, and check your solution by plugging it back into the original equation. With practice, you'll become a pro at solving linear equations!