Activity 1: Complete Each Solution By Filling In The Blank With The Correct Answer.1. Solve For $x$: $\[ \begin{array}{l} X + 6 = 10 \\ X + 6 - 6 = 10 - 6 \\ X = \_ \end{array} \\]2. Solve For $y$:

Feb 26, 2025 by ADMIN 224 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 linear equations by filling in the blank with the correct answer. We will use two examples to demonstrate the step-by-step process of solving linear equations.

Example 1: Solving for x

Step 1: Write the equation

The given equation is $x + 6 = 10$ . Our goal is to solve for $x$ .

Step 2: Subtract 6 from both sides

To isolate $x$ , we need to get rid of the constant term on the left side of the equation. We can do this by subtracting 6 from both sides of the equation.

x + 6 - 6 = 10 - 6

Step 3: Simplify the equation

After subtracting 6 from both sides, the equation becomes:

x = 4

Solution

The correct answer is $\boxed{4}$ .

Example 2: Solving for y

Step 1: Write the equation

The given equation is $y - 3 = 7$ . Our goal is to solve for $y$ .

Step 2: Add 3 to both sides

To isolate $y$ , we need to get rid of the constant term on the left side of the equation. We can do this by adding 3 to both sides of the equation.

y - 3 + 3 = 7 + 3

Step 3: Simplify the equation

After adding 3 to both sides, the equation becomes:

y = 10

Solution

The correct answer is $\boxed{10}$ .

Tips and Tricks

When solving linear equations, always follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
To isolate a variable, you can add, subtract, multiply, or divide both sides of the equation by the same value.
When simplifying an equation, make sure to combine like terms and eliminate any unnecessary constants.

Conclusion

Solving linear equations is a fundamental skill in mathematics that requires practice and patience. By following the step-by-step process outlined in this article, you can become proficient in solving linear equations and tackle more complex math problems with confidence. Remember to always follow the order of operations and simplify equations carefully to ensure accurate solutions.

Frequently Asked Questions

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1. For example, $x + 2 = 5$ is a linear equation.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow the step-by-step process outlined in this article: write the equation, isolate the variable, and simplify the equation.

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

A: A linear equation has a highest power of 1, while a quadratic equation has a highest power of 2. For example, $x^2 + 2x = 5$ is a quadratic equation.

Glossary

Linear equation: An equation in which the highest power of the variable(s) is 1.
Variable: A letter or symbol that represents a value that can change.
Constant: A value that does not change.
Simplify: To reduce an equation to its simplest form by combining like terms and eliminating unnecessary constants.

References

Math Open Reference
Khan Academy
Mathway
Solving Linear Equations: A Q&A Guide =====================================

Introduction

Solving linear equations is a fundamental skill in mathematics that requires practice and patience. In this article, we will provide a comprehensive Q&A guide to help you understand and master the concept of solving 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. For example, $x + 2 = 5$ is a linear equation.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow the step-by-step process outlined below:

Write the equation
Isolate the variable
Simplify the equation

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

A: A linear equation has a highest power of 1, while a quadratic equation has a highest power of 2. For example, $x^2 + 2x = 5$ is a quadratic equation.

Q: How do I isolate a variable in a linear equation?

A: To isolate a variable in a linear equation, you can add, subtract, multiply, or divide both sides of the equation by the same value. For example, to isolate $x$ in the equation $x + 2 = 5$ , you can subtract 2 from both sides:

x + 2 - 2 = 5 - 2
x = 3

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 you have multiple operations in an expression. 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 simplify an equation?

A: To simplify an equation, combine like terms and eliminate any unnecessary constants. For example, to simplify the equation $x + 2 + 3 = 5$ , you can combine the like terms:

x + 5 = 5

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 isolating the variable correctly
Not simplifying the equation correctly
Not checking the solution to make sure it is correct

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 make sure it is true. For example, if you solve the equation $x + 2 = 5$ and get $x = 3$ , you can plug $x = 3$ back into the original equation to check:

3 + 2 = 5
5 = 5

Since the equation is true, you know that your solution is correct.

Conclusion

Solving linear equations is a fundamental skill in mathematics that requires practice and patience. By following the step-by-step process outlined in this article and avoiding common mistakes, you can become proficient in solving linear equations and tackle more complex math problems with confidence.

Frequently Asked Questions

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable(s) is 1.

Q: How do I solve a linear equation?

A: To solve a linear equation, follow the step-by-step process outlined in this article.

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

A: A linear equation has a highest power of 1, while a quadratic equation has a highest power of 2.

Glossary

Linear equation: An equation in which the highest power of the variable(s) is 1.
Variable: A letter or symbol that represents a value that can change.
Constant: A value that does not change.
Simplify: To reduce an equation to its simplest form by combining like terms and eliminating unnecessary constants.