What Are The Possible Steps Involved In Solving The Equation Shown? Select Three Options.$3.5 + 1.2(6.3 - 7x) = 9.38$A. Add 3.5 And 1.2.B. Distribute 1.2 To 6.3 And \[$-7x\$\].C. Combine 6.3 And \[$-7x\$\].D. Combine 3.5 And

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 explore the possible steps involved in solving a linear equation, using the equation $3.5 + 1.2(6.3 - 7x) = 9.38$ as an example. We will examine three options and discuss the correct approach to solving this equation.

Understanding the Equation

Before we dive into the solution, let's break down the equation and understand its components. The equation is a linear equation, which means it can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. In this case, the equation is $3.5 + 1.2(6.3 - 7x) = 9.38$. We can see that the equation involves addition, multiplication, and subtraction.

Option A: Add 3.5 and 1.2

Option A suggests adding 3.5 and 1.2. However, this is not the correct approach to solving the equation. When we add 3.5 and 1.2, we get 4.7, but this does not help us solve the equation. In fact, adding 3.5 and 1.2 would be a step in the wrong direction, as it would not allow us to isolate the variable $x$.

Option B: Distribute 1.2 to 6.3 and $-7x$

Option B suggests distributing 1.2 to 6.3 and $-7x$. This is a correct step in solving the equation. When we distribute 1.2 to 6.3 and $-7x$, we get $7.56 - 8.4x$. This step is essential in simplifying the equation and making it easier to solve.

Option C: Combine 6.3 and $-7x$

Option C suggests combining 6.3 and $-7x$. However, this is not the correct approach to solving the equation. Combining 6.3 and $-7x$ would result in $-0.7x + 6.3$, but this would not help us solve the equation. In fact, combining 6.3 and $-7x$ would be a step in the wrong direction, as it would not allow us to isolate the variable $x$.

The Correct Approach

The correct approach to solving the equation is to follow the order of operations (PEMDAS). We start by distributing 1.2 to 6.3 and $-7x$, which gives us $7.56 - 8.4x$. Next, we can combine the constants on the left-hand side of the equation, which gives us $3.5 + 7.56 = 11.06$. Finally, we can subtract 9.38 from both sides of the equation, which gives us $11.06 - 9.38 = 1.68$. This allows us to isolate the variable $x$ and solve for its value.

Solving for $x$

Now that we have isolated the variable $x$, we can solve for its value. We have the equation $1.68 = -8.4x$. To solve for $x$, we can divide both sides of the equation by $-8.4$, which gives us $x = -1.68 / 8.4 = -0.2$. Therefore, the value of $x$ is $-0.2$.

Conclusion

In conclusion, solving linear equations requires a step-by-step approach. We must follow the order of operations (PEMDAS) and isolate the variable $x$ to solve for its value. In this article, we examined three options for solving the equation $3.5 + 1.2(6.3 - 7x) = 9.38$ and discussed the correct approach to solving this equation. By following the correct steps, we can solve for the value of $x$ and understand the underlying mathematics of the equation.

Additional Tips and Resources

• To solve linear equations, it's essential to follow the order of operations (PEMDAS).
• Isolate the variable $x$ by adding, subtracting, multiplying, or dividing both sides of the equation.
• Use inverse operations to solve for the value of $x$.
• Practice solving linear equations to become proficient in this skill.
• For additional resources and practice problems, visit Khan Academy's Linear Equations page.

Final Thoughts

Introduction

In our previous article, we explored the possible steps involved in solving a linear equation, using the equation $3.5 + 1.2(6.3 - 7x) = 9.38$ as an example. We discussed the correct approach to solving this equation and provided additional tips and resources for solving linear equations. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

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

A: To isolate the variable $x$ in a linear equation, you need to get $x$ by itself on one side of the equation. You can do this by adding, subtracting, multiplying, or dividing both sides of the equation by the same value. For example, if you have the equation $2x + 3 = 5$, you can subtract 3 from both sides to get $2x = 2$, and then divide both sides by 2 to get $x = 1$.

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. For example, the equation $2x + 3 = 5$ is a linear equation. A quadratic equation, on the other hand, is an equation in which the highest power of the variable is 2. For example, 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 get rid of the fractions by multiplying both sides of the equation by the denominator. For example, if you have the equation $\frac{1}{2}x + 2 = 3$, you can multiply both sides by 2 to get $x + 4 = 6$, and then subtract 4 from both sides to get $x = 2$.

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 plugging the solution back into the original equation to make sure it's true.

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 $x$ on one side of the equation
• Not checking your work by plugging the solution back into the original equation
• Not using inverse operations to solve for the value of $x$

Conclusion

Solving linear equations is a fundamental skill in mathematics, and it requires a step-by-step approach. By following the correct steps and using inverse operations, we can solve for the value of $x$ and understand the underlying mathematics of the equation. In this article, we answered some frequently asked questions about solving linear equations and provided additional tips and resources for solving linear equations.

Additional Tips and Resources

• To solve linear equations, it's essential to follow the order of operations (PEMDAS).
• Isolate the variable $x$ by adding, subtracting, multiplying, or dividing both sides of the equation.
• Use inverse operations to solve for the value of $x$.
• Practice solving linear equations to become proficient in this skill.
• For additional resources and practice problems, visit Khan Academy's Linear Equations page.

Final Thoughts

Solving linear equations is a fundamental skill in mathematics, and it requires a step-by-step approach. By following the correct steps and using inverse operations, we can solve for the value of $x$ and understand the underlying mathematics of the equation. With practice and patience, anyone can become proficient in solving linear equations and apply this skill to real-world problems.