Solve The Equation:$\[ 2x - 10 = 24 \\]

Feb 26, 2025 by ADMIN 40 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 and professionals alike. In this article, we will focus on solving a specific linear equation, $2x - 10 = 24$ , and provide a step-by-step guide on how to approach it.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants, and $x$ is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation to be Solved

The equation we will be solving is $2x - 10 = 24$ . This is a linear equation in one variable, $x$ . Our goal is to isolate the variable $x$ and find its value.

Step 1: Add 10 to Both Sides

To solve the equation, we need to isolate the variable $x$ . The first step is to add 10 to both sides of the equation. This will eliminate the negative term on the left-hand side.

${ 2x - 10 + 10 = 24 + 10 }$

Simplifying the equation, we get:

${ 2x = 34 }$

Step 2: Divide Both Sides by 2

Now that we have isolated the term with the variable, we need to get rid of the coefficient, 2. We can do this by dividing both sides of the equation by 2.

${ \frac{2x}{2} = \frac{34}{2} }$

Simplifying the equation, we get:

${ x = 17 }$

Conclusion

In this article, we solved the linear equation $2x - 10 = 24$ using algebraic manipulation. We added 10 to both sides of the equation to eliminate the negative term, and then divided both sides by 2 to isolate the variable $x$ . The final solution is $x = 17$ .

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 avoid errors, make sure to add or subtract the same value to both sides of the equation.
When dividing both sides of the equation by a coefficient, make sure to simplify the fraction.

Real-World Applications

Linear equations have numerous 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.

Common Mistakes to Avoid

When solving linear equations, it's essential to avoid common mistakes, including:

Not following the order of operations (PEMDAS)
Adding or subtracting different values to both sides of the equation
Not simplifying fractions when dividing both sides of the equation

Practice Problems

To practice solving linear equations, try the following problems:

Solve the equation $3x + 2 = 11$
Solve the equation $x - 4 = 9$
Solve the equation $2x + 5 = 17$

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article, you can solve linear equations with ease. Remember to follow the order of operations (PEMDAS), add or subtract the same value to both sides of the equation, and simplify fractions when dividing both sides of the equation. With practice, you'll become proficient in solving linear equations and be able to apply them to real-world problems.

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Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. It can be written in the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants, and $x$ is the variable.

Q: How do I solve a linear equation?

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

Add or subtract the same value to both sides of the equation to isolate the variable.
Multiply or divide both sides of the equation by the same value to eliminate the coefficient.
Simplify the equation to find the value of the variable.

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 handle fractions when solving linear equations?

A: When solving linear equations, you may encounter fractions. To handle fractions, follow these steps:

Multiply both sides of the equation by the denominator of the fraction to eliminate the fraction.
Simplify the equation to find the value of the variable.

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)
Adding or subtracting different values to both sides of the equation
Not simplifying fractions when dividing both sides of the equation

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

A: To check your solution to a linear equation, plug the value of the variable back into the original equation and simplify. If the equation is true, then your solution is correct.

Q: Can I use a calculator to solve linear equations?

A: Yes, you can use a calculator to solve linear equations. However, make sure to follow the order of operations (PEMDAS) and check your solution to ensure it is correct.

Q: What are some real-world applications of linear equations?

A: Linear equations have numerous 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.

Q: How can I practice solving linear equations?

A: To practice solving linear equations, try the following:

Solve linear equations with different coefficients and constants.
Use online resources, such as math websites and apps, to practice solving linear equations.
Work with a partner or tutor to practice solving linear equations.

Conclusion

Solving linear equations is a crucial skill for students and professionals alike. By following the steps outlined in this article and practicing regularly, you can become proficient in solving linear equations and apply them to real-world problems.