Solve For { K $} . . . { 9k = 36 \}

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Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill to master. In this article, we will focus on solving a simple linear equation to find the value of k. We will break down the problem step by step, using clear and concise language to ensure that you understand the process.

What is a Linear Equation?

A linear equation is an equation in which the highest power of the variable (in this case, k) is 1. It is a simple equation that can be solved using basic algebraic operations. The general form of a linear equation is:

ax + b = c

where a, b, and c are constants, and x is the variable.

The Problem

In this problem, we are given the equation:

9k = 36

Our goal is to solve for k, which means we need to isolate k on one side of the equation.

Step 1: Understand the Equation

The first step in solving the equation is to understand what it means. In this case, the equation states that 9 times k is equal to 36. We need to find the value of k that makes this equation true.

Step 2: Divide Both Sides by 9

To solve for k, we need to isolate k on one side of the equation. We can do this by dividing both sides of the equation by 9. This will cancel out the 9 on the left-hand side of the equation, leaving us with k on its own.

9k = 36

k = 36 ÷ 9

Step 3: Simplify the Right-Hand Side

Now that we have divided both sides of the equation by 9, we need to simplify the right-hand side. In this case, we can simplify 36 ÷ 9 by dividing 36 by 9.

36 ÷ 9 = 4

So, the equation now becomes:

k = 4

Conclusion

In this article, we solved a simple linear equation to find the value of k. We broke down the problem step by step, using clear and concise language to ensure that you understand the process. By following these steps, you can solve linear equations with ease.

Tips and Tricks

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

  • Understand the equation: Before you start solving the equation, make sure you understand what it means.
  • Isolate the variable: To solve for the variable, you need to isolate it on one side of the equation.
  • Use inverse operations: To isolate the variable, you can use inverse operations such as addition, subtraction, multiplication, and division.
  • Simplify the right-hand side: Once you have isolated the variable, simplify the right-hand side of the equation.

Practice Problems

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

  • 2x + 5 = 11
  • 4y - 3 = 7
  • 6z + 2 = 14

Try solving these problems using the steps outlined in this article. If you get stuck, don't hesitate to ask for help.

Conclusion

Introduction

In our previous article, we covered the basics of solving linear equations. However, we know that you may still have some questions. In this article, we will answer some of the most frequently asked questions about solving linear equations.

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable (in this case, k) is 1. It is a simple equation that can be solved using basic algebraic operations.

Q: How do I know if an equation is linear?

A: To determine if an equation is linear, look for the following characteristics:

  • The equation has only one variable (in this case, k).
  • The highest power of the variable is 1.
  • The equation can be written in the form ax + b = c, where a, b, and c are constants.

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 is 1, while a quadratic equation is an equation in which the highest power of the variable is 2. For example:

Linear equation: 2x + 3 = 5 Quadratic equation: x^2 + 4x + 4 = 0

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

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

  1. Multiply both sides of the equation by the least common multiple (LCM) of the denominators.
  2. Simplify the equation.
  3. Solve for the variable.

For example:

1/2x + 1/3 = 2/3

Multiply both sides by 6 (the LCM of 2 and 3):

3x + 2 = 4

Simplify the equation:

3x = 2

Solve for x:

x = 2/3

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

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

  1. Multiply both sides of the equation by 10 to eliminate the decimals.
  2. Simplify the equation.
  3. Solve for the variable.

For example:

0.5x + 2 = 3.5

Multiply both sides by 10:

5x + 20 = 35

Simplify the equation:

5x = 15

Solve for x:

x = 3

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

A: Yes, you can use a calculator to solve linear equations. However, it's always a good idea to check your work by hand to make sure you understand the solution.

Q: What if I have a linear equation with a negative coefficient?

A: If you have a linear equation with a negative coefficient, simply multiply both sides of the equation by -1 to eliminate the negative sign.

For example:

-2x + 3 = 5

Multiply both sides by -1:

2x - 3 = -5

Simplify the equation:

2x = -2

Solve for x:

x = -1

Conclusion

We hope this article has answered some of the most frequently asked questions about solving linear equations. Remember to practice solving linear equations to become more confident and proficient in your math skills. If you have any more questions, don't hesitate to ask.