Complete: Week 3 Lesson 2 Interactive BSolve: 2 + X = − 8 2 + X = -8 2 + X = − 8

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Introduction

Solving linear equations is a fundamental concept in mathematics that forms the basis of various mathematical operations. It is essential to understand and apply this concept to solve equations involving one or more variables. In this article, we will focus on solving linear equations, specifically the equation 2+x=−82 + x = -8. We will break down the solution process into manageable steps and provide a clear explanation of each step.

What are Linear Equations?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form ax+b=cax + b = c, where aa, bb, and cc are constants, and xx is the variable. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

The Equation 2+x=−82 + x = -8

The equation 2+x=−82 + x = -8 is a linear equation in which the variable xx is isolated on one side of the equation. To solve for xx, we need to isolate the variable on one side of the equation. We can do this by subtracting 2 from both sides of the equation.

Step 1: Subtract 2 from Both Sides

To isolate the variable xx, we need to subtract 2 from both sides of the equation. This will give us:

2+x−2=−8−22 + x - 2 = -8 - 2

Simplifying the equation, we get:

x=−10x = -10

Step 2: Check the Solution

To verify that our solution is correct, we can plug it back into the original equation. If the equation holds true, then our solution is correct.

2+x=−82 + x = -8

Substituting x=−10x = -10 into the equation, we get:

2+(−10)=−82 + (-10) = -8

Simplifying the equation, we get:

−8=−8-8 = -8

Since the equation holds true, our solution is correct.

Conclusion

Solving linear equations is a crucial concept in mathematics that requires a clear understanding of the solution process. In this article, we focused on solving the equation 2+x=−82 + x = -8 using algebraic manipulation. We broke down the solution process into manageable steps and provided a clear explanation of each step. By following these steps, you can solve linear equations with ease and apply this concept to various mathematical operations.

Interactive BSolve: 2+x=−82 + x = -8

Step 1: Subtract 2 from Both Sides

To isolate the variable xx, we need to subtract 2 from both sides of the equation. This will give us:

2+x−2=−8−22 + x - 2 = -8 - 2

Simplifying the equation, we get:

x=−10x = -10

Step 2: Check the Solution

To verify that our solution is correct, we can plug it back into the original equation. If the equation holds true, then our solution is correct.

2+x=−82 + x = -8

Substituting x=−10x = -10 into the equation, we get:

2+(−10)=−82 + (-10) = -8

Simplifying the equation, we get:

−8=−8-8 = -8

Since the equation holds true, our solution is correct.

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, you need to isolate the variable on one side of the equation using algebraic manipulation.

Q: What is the solution to the equation 2+x=−82 + x = -8?

A: The solution to the equation 2+x=−82 + x = -8 is x=−10x = -10.

Additional Resources

Conclusion

Solving linear equations is a fundamental concept in mathematics that requires a clear understanding of the solution process. In this article, we focused on solving the equation 2+x=−82 + x = -8 using algebraic manipulation. We broke down the solution process into manageable steps and provided a clear explanation of each step. By following these steps, you can solve linear equations with ease and apply this concept to various mathematical operations.

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Introduction

Solving linear equations is a fundamental concept in mathematics that forms the basis of various mathematical operations. In our previous article, we provided a step-by-step guide to solving the equation 2+x=−82 + x = -8. In this article, we will provide a Q&A guide to help you understand and apply the concept of solving linear equations.

Q&A Guide

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, you need to isolate the variable on one side of the equation using algebraic manipulation.

Q: What is the solution to the equation 2+x=−82 + x = -8?

A: The solution to the equation 2+x=−82 + x = -8 is x=−10x = -10.

Q: How do I check if my solution is correct?

A: To verify that your solution is correct, you can plug it back into the original equation. If the equation holds true, then your solution is correct.

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.

Q: How do I solve a linear equation with fractions?

A: To solve a linear equation with fractions, you need to eliminate the fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators.

Q: What is the LCM of 2 and 3?

A: The LCM of 2 and 3 is 6.

Q: How do I solve a linear equation with decimals?

A: To solve a linear equation with decimals, you need to eliminate the decimals by multiplying both sides of the equation by a power of 10.

Q: What is the difference between a linear equation and a system of linear equations?

A: A linear equation is a single equation with one variable, while a system of linear equations is a set of two or more equations with two or more variables.

Q: How do I solve a system of linear equations?

A: To solve a system of linear equations, you need to use substitution or elimination methods to find the values of the variables.

Examples

Example 1: Solving a Linear Equation with Fractions

Solve the equation 12x+3=5\frac{1}{2}x + 3 = 5.

Step 1: Multiply both sides of the equation by 2

12x+3=5\frac{1}{2}x + 3 = 5

2(12x+3)=2(5)2(\frac{1}{2}x + 3) = 2(5)

x+6=10x + 6 = 10

Step 2: Subtract 6 from both sides of the equation

x+6−6=10−6x + 6 - 6 = 10 - 6

x=4x = 4

Example 2: Solving a Linear Equation with Decimals

Solve the equation 2.5x+3=72.5x + 3 = 7.

Step 1: Multiply both sides of the equation by 10

2.5x+3=72.5x + 3 = 7

10(2.5x+3)=10(7)10(2.5x + 3) = 10(7)

25x+30=7025x + 30 = 70

Step 2: Subtract 30 from both sides of the equation

25x+30−30=70−3025x + 30 - 30 = 70 - 30

25x=4025x = 40

Step 3: Divide both sides of the equation by 25

25x25=4025\frac{25x}{25} = \frac{40}{25}

x=85x = \frac{8}{5}

Conclusion

Solving linear equations is a fundamental concept in mathematics that requires a clear understanding of the solution process. In this article, we provided a Q&A guide to help you understand and apply the concept of solving linear equations. We also provided examples of solving linear equations with fractions and decimals. By following these steps and examples, you can solve linear equations with ease and apply this concept to various mathematical operations.

Additional Resources

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, you need to isolate the variable on one side of the equation using algebraic manipulation.

Q: What is the solution to the equation 2+x=−82 + x = -8?

A: The solution to the equation 2+x=−82 + x = -8 is x=−10x = -10.

Q: How do I check if my solution is correct?

A: To verify that your solution is correct, you can plug it back into the original equation. If the equation holds true, then your solution is correct.

Conclusion

Solving linear equations is a fundamental concept in mathematics that requires a clear understanding of the solution process. In this article, we provided a Q&A guide to help you understand and apply the concept of solving linear equations. We also provided examples of solving linear equations with fractions and decimals. By following these steps and examples, you can solve linear equations with ease and apply this concept to various mathematical operations.