Solve For X: $\[ 3x - 1 = -10 \\]A. \[$ X = 3 \$\] B. \[$ X = -3 \$\] C. \[$ X = 4 \$\] D. \[$ X = -4 \$\]

by ADMIN 110 views

Introduction

Solving for x is a fundamental concept in algebra that involves isolating the variable x in a linear equation. In this article, we will focus on solving a simple linear equation of the form 3x - 1 = -10. We will use a step-by-step approach to solve for x and provide a clear explanation of each step.

What is a Linear Equation?

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 = c, where a, b, and c are constants. Linear equations can be solved using basic algebraic operations such as addition, subtraction, multiplication, and division.

The Equation to Solve

The equation we will be solving is 3x - 1 = -10. This is a linear equation in which the highest power of the variable x is 1.

Step 1: Add 1 to Both Sides

To solve for x, we need to isolate the variable x on one side of the equation. The first step is to add 1 to both sides of the equation. This will eliminate the negative term on the left-hand side of the equation.

3x - 1 + 1 = -10 + 1

Simplifying the equation, we get:

3x = -9

Step 2: Divide Both Sides by 3

Now that we have isolated the term 3x on the left-hand side of the equation, we can divide both sides by 3 to solve for x.

(3x) / 3 = (-9) / 3

Simplifying the equation, we get:

x = -3

Conclusion

In this article, we solved a simple linear equation of the form 3x - 1 = -10 using a step-by-step approach. We added 1 to both sides of the equation to eliminate the negative term, and then divided both sides by 3 to solve for x. The solution to the equation is x = -3.

Answer Options

Now that we have solved the equation, let's take a look at the answer options:

A. x = 3 B. x = -3 C. x = 4 D. x = -4

Based on our solution, we can see that the correct answer is:

B. x = -3

Why is this the Correct Answer?

The correct answer is x = -3 because we solved the equation 3x - 1 = -10 using a step-by-step approach, and we arrived at the solution x = -3. This is the only answer option that matches our solution.

Tips and Tricks

Here are some tips and tricks to help you solve linear equations:

  • Always add or subtract the same value to both sides of the equation.
  • Always multiply or divide both sides of the equation by the same value.
  • Use inverse operations to isolate the variable x.
  • Check your solution by plugging it back into the original equation.

Conclusion

Introduction

In our previous article, we solved a simple linear equation of the form 3x - 1 = -10 using a step-by-step approach. In this article, we will provide a Q&A guide to help you understand the concept of solving linear equations and provide additional examples to practice.

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 is 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, you need to isolate the variable x on one side of the equation. You can do this by using basic algebraic operations such as addition, subtraction, multiplication, and division.

Q: What are the steps to solve a linear equation?

A: The steps to solve a linear equation are:

  1. Add or subtract the same value to both sides of the equation to eliminate any constants.
  2. Multiply or divide both sides of the equation by the same value to isolate the variable x.
  3. Use inverse operations to isolate the variable x.
  4. Check your solution by plugging it back into the original equation.

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 + 3 = 5 is a linear equation, while the equation x^2 + 4x + 4 = 0 is a quadratic equation.

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 least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest multiple that is common to two or more numbers. For example, 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 are some common mistakes to avoid when solving linear equations?

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

  • Not isolating the variable x on one side of the equation.
  • Not using inverse operations to isolate the variable x.
  • Not checking the solution by plugging it back into the original equation.

Q: How do I check my solution?

A: To check your solution, you need to plug it back into the original equation and verify that it is true.

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

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

  • Physics: Linear equations are used to describe the motion of objects.
  • Engineering: Linear equations are used to design and optimize systems.
  • Economics: Linear equations are used to model economic systems.

Conclusion

Solving linear equations is a fundamental concept in algebra that has many real-world applications. In this article, we provided a Q&A guide to help you understand the concept of solving linear equations and provide additional examples to practice. We hope this article has been helpful in your understanding of linear equations.

Practice Problems

Here are some practice problems to help you practice solving linear equations:

  1. Solve the equation 2x + 5 = 11.
  2. Solve the equation x - 3 = 7.
  3. Solve the equation 4x - 2 = 14.
  4. Solve the equation x + 2 = 9.
  5. Solve the equation 3x + 1 = 12.

Answer Key

Here are the answers to the practice problems:

  1. x = 3
  2. x = 10
  3. x = 4
  4. x = 7
  5. x = 3.67