Select The Best Answer For The Question.18. Solve The Equation: 7 X = 42 7x = 42 7 X = 42 .A. X = 6 X = 6 X = 6 B. X = − 6 X = -6 X = − 6 C. X = − 7 X = -7 X = − 7 D. X = 7 X = 7 X = 7

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, $7x = 42$, and provide a step-by-step guide on how to arrive at the correct solution.

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 $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable.

The Equation $7x = 42$

The equation $7x = 42$ is a simple linear equation, where the coefficient of $x$ is 7, and the constant term is 42. To solve for $x$, we need to isolate the variable on one side of the equation.

Step 1: Divide Both Sides by 7

To isolate $x$, we need to get rid of the coefficient 7 that is multiplied by $x$. We can do this by dividing both sides of the equation by 7.

$$\frac{7x}{7} = \frac{42}{7}$$

Step 2: Simplify the Equation

After dividing both sides by 7, we get:

$$x = 6$$

The Correct Solution

Therefore, the correct solution to the equation $7x = 42$ is $x = 6$.

Why is $x = 6$ the Correct Solution?

To understand why $x = 6$ is the correct solution, let's think about what the equation $7x = 42$ means. The equation states that 7 times $x$ is equal to 42. In other words, if we multiply 7 by a number, we get 42. The only number that satisfies this condition is 6, because $7 \times 6 = 42$.

Conclusion

Solving linear equations is a crucial skill for students to master, and it requires a step-by-step approach. By following the steps outlined in this article, we can arrive at the correct solution to the equation $7x = 42$, which is $x = 6$. Remember, the key to solving linear equations is to isolate the variable on one side of the equation, and to simplify the equation by performing the necessary operations.

Common Mistakes to Avoid

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

• Not isolating the variable: Make sure to isolate the variable on one side of the equation.
• Not simplifying the equation: Make sure to simplify the equation by performing the necessary operations.
• Not checking the solution: Make sure to check the solution by plugging it back into the original equation.

Practice Problems

Here are a few practice problems to help you reinforce your understanding of solving linear equations:

1. Solve the equation $4x = 24$.
2. Solve the equation $3x = 18$.
3. Solve the equation $2x = 12$.

Answer Key

1. $x = 6$
2. $x = 6$
3. $x = 6$

Conclusion

$$$$

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 $ax = b$, where $a$ and $b$ are constants, and $x$ is the variable.

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. This can be done by performing the necessary operations, such as addition, subtraction, multiplication, and division.

Q: What is the first step in solving a linear equation?

A: The first step in solving a linear equation is to isolate the variable on one side of the equation. This can be done by performing the necessary operations, such as addition, subtraction, multiplication, and division.

Q: How do I know which operation to perform?

A: To determine which operation to perform, you need to look at the equation and identify the coefficient of the variable. The coefficient is the number that is multiplied by the variable. Once you have identified the coefficient, you can perform the necessary operation to isolate the variable.

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 is an equation in which the highest power of the variable (in this case, $x$) is 2. For example, the equation $x^2 + 4x + 4 = 0$ is a quadratic equation, while the equation $2x + 3 = 5$ is a linear equation.

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

A: Yes, you can use a calculator to solve a linear equation. However, it is always a good idea to check your answer by plugging it back into the original equation.

Q: What is the importance of solving linear equations?

A: Solving linear equations is an important skill in mathematics and is used in a wide range of applications, including science, engineering, and economics. It is also a fundamental concept in algebra and is used to solve more complex equations.

Q: Can I solve a linear equation with a negative coefficient?

A: Yes, you can solve a linear equation with a negative coefficient. For example, the equation $-3x = 12$ can be solved by dividing both sides by -3.

Q: Can I solve a linear equation with a fraction coefficient?

A: Yes, you can solve a linear equation with a fraction coefficient. For example, the equation $\frac{1}{2}x = 3$ can be solved by multiplying both sides by 2.

Q: What is the final step in solving a linear equation?

A: The final step in solving a linear equation is to check your answer by plugging it back into the original equation. This ensures that your solution is correct and that you have not made any mistakes.

Conclusion

Solving linear equations is an important skill in mathematics and is used in a wide range of applications. By following the steps outlined in this article, you can solve linear equations with ease and confidence. Remember to always check your answer by plugging it back into the original equation to ensure that your solution is correct.

Practice Problems

Here are a few practice problems to help you reinforce your understanding of solving linear equations:

1. Solve the equation $2x + 3 = 7$.
2. Solve the equation $x - 2 = 5$.
3. Solve the equation $3x = 12$.

Answer Key

1. $x = 2$
2. $x = 7$
3. $x = 4$

Conclusion

Solving linear equations is an important skill in mathematics and is used in a wide range of applications. By following the steps outlined in this article, you can solve linear equations with ease and confidence. Remember to always check your answer by plugging it back into the original equation to ensure that your solution is correct.