Solve For $x$: $x - 10 = -12$A. $x = 2$ B. $x = -2$ C. $x = 22$ D. $x = -22$

Feb 26, 2025 by ADMIN 82 views

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

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 of the form $x - 10 = -12$ . We will break down the solution step by step, and by the end of this article, you will be able to solve similar equations with ease.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, $x$ ) is 1. Linear equations can be written in the form $ax + b = c$ , where $a$ , $b$ , and $c$ are constants. In our example equation, $x - 10 = -12$ , we can see that the highest power of $x$ is 1, making it a linear equation.

Step 1: Add 10 to Both Sides

To solve the equation $x - 10 = -12$ , 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.

x - 10 + 10 = -12 + 10

By adding 10 to both sides, we get:

x = -2

Step 2: Simplify the Equation

Now that we have added 10 to both sides, we can simplify the equation by combining like terms. In this case, there are no like terms to combine, so the equation remains the same.

Step 3: Check the Solution

To ensure that our solution is correct, we need to check it by plugging it back into the original equation. If the solution is correct, the equation should hold true.

x - 10 = -12
-2 - 10 = -12
-12 = -12

As we can see, the solution $x = -2$ satisfies the original equation, making it the correct solution.

Conclusion

Solving linear equations is a straightforward process that requires attention to detail and a step-by-step approach. By following the steps outlined in this article, you can solve linear equations of the form $ax + b = c$ with ease. Remember to add or subtract the same value from both sides of the equation to isolate the variable, and always check your solution by plugging it back into the original equation.

Common Mistakes to Avoid

When solving linear equations, there are several common mistakes to avoid. Here are a few:

Not adding or subtracting the same value from both sides: Make sure to add or subtract the same value from both sides of the equation to maintain the equality.
Not simplifying the equation: Simplify the equation by combining like terms to make it easier to solve.
Not checking the solution: Always check your solution by plugging it back into the original equation to ensure that it satisfies the equation.

Practice Problems

To practice solving linear equations, try the following problems:

$x + 5 = 10$
$x - 3 = 7$
$2x = 12$

Answer Key

Here are the answers to the practice problems:

$x = 5$
$x = 10$
$x = 6$

Conclusion

Solving linear equations is a fundamental skill that requires attention to detail and a step-by-step approach. By following the steps outlined in this article and avoiding common mistakes, you can solve linear equations with ease. Remember to practice regularly to build your skills and confidence in solving linear equations.

Final Answer

Introduction

In our previous article, we covered the basics of solving linear equations of the form $ax + b = c$ . In this article, we will provide a Q&A guide to help you better understand the concept and solve linear equations with ease.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, $x$ ) is 1. Linear equations 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, you need to isolate the variable $x$ . You can do this by adding or subtracting the same value from both sides of the equation. For example, if you have the equation $x - 10 = -12$ , you can add 10 to both sides to get $x = -2$ .

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 (in this case, $x$ ) is 1. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: How do I simplify a linear equation?

A: To simplify a linear equation, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, if you have the equation $x + 3x = 5x$ , you can combine the like terms to get $4x = 5x$ .

Q: What is the order of operations in solving linear equations?

A: The order of operations in solving linear equations is:

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 check my solution to a linear equation?

A: To check your solution to a linear equation, you need to plug it back into the original equation. If the solution is correct, the equation should hold true. For example, if you have the equation $x - 10 = -12$ and you solve it to get $x = -2$ , you can plug $x = -2$ back into the original equation to check that it is 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 adding or subtracting the same value from both sides of the equation.
Not simplifying the equation by combining like terms.
Not checking the solution by plugging it back into the original equation.

Q: How can I practice solving linear equations?

A: You can practice solving linear equations by working through practice problems. You can find practice problems in your textbook or online. You can also try solving linear equations on your own by creating your own problems.

Conclusion

Final Answer

The final answer is: $\boxed{-2}$