What Are The Possible Steps Involved In Solving The Equation Shown? Select Three Options. 3.5 + 1.2 ( 6.3 − 7 X ) = 9.38 3.5 + 1.2(6.3 - 7x) = 9.38 3.5 + 1.2 ( 6.3 − 7 X ) = 9.38 A. Distribute 1.2 To 6.3 And { -7x$}$.B. Combine 6.3 And { -7x$}$.C. Combine 3.5 And 7.56.D. Subtract

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 for solving this equation and discuss the correct approach.

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 is an equation in which the highest power of the variable (in this case, x) is 1. The equation is:

$3.5 + 1.2(6.3 - 7x) = 9.38$

This equation involves addition, multiplication, and subtraction. To solve it, we need to follow the order of operations (PEMDAS):

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

Option A: Distribute 1.2 to 6.3 and -7x

One possible approach to solving this equation is to distribute the 1.2 to both 6.3 and -7x. This involves multiplying 1.2 by each of these terms separately.

Step 1: Distribute 1.2 to 6.3

$1.2 \times 6.3 = 7.56$

Step 2: Distribute 1.2 to -7x

$1.2 \times -7x = -8.4x$

Now, we can rewrite the equation as:

$3.5 + 7.56 - 8.4x = 9.38$

Step 3: Combine like terms

$3.5 + 7.56 = 11.06$

So, the equation becomes:

$11.06 - 8.4x = 9.38$

Step 4: Subtract 11.06 from both sides

$-8.4x = -1.68$

Step 5: Divide both sides by -8.4

$x = \frac{-1.68}{-8.4}$

$x = 0.2$

This is one possible solution to the equation.

Option B: Combine 6.3 and -7x

Another possible approach to solving this equation is to combine 6.3 and -7x. This involves adding these two terms together.

$6.3 - 7x = -0.7x + 6.3$

Now, we can rewrite the equation as:

$3.5 + 1.2(-0.7x + 6.3) = 9.38$

Step 1: Distribute 1.2 to -0.7x and 6.3

$1.2 \times -0.7x = -0.84x$

$1.2 \times 6.3 = 7.56$

Now, we can rewrite the equation as:

$3.5 - 0.84x + 7.56 = 9.38$

Step 2: Combine like terms

$3.5 + 7.56 = 11.06$

So, the equation becomes:

$11.06 - 0.84x = 9.38$

Step 3: Subtract 11.06 from both sides

$-0.84x = -1.68$

Step 4: Divide both sides by -0.84

$x = \frac{-1.68}{-0.84}$

$x = 2$

This is another possible solution to the equation.

Option C: Combine 3.5 and 7.56

A third possible approach to solving this equation is to combine 3.5 and 7.56. This involves adding these two terms together.

$3.5 + 7.56 = 11.06$

Now, we can rewrite the equation as:

$11.06 + 1.2(6.3 - 7x) = 9.38$

Step 1: Distribute 1.2 to 6.3 and -7x

$1.2 \times 6.3 = 7.56$

$1.2 \times -7x = -8.4x$

Now, we can rewrite the equation as:

$11.06 + 7.56 - 8.4x = 9.38$

Step 2: Combine like terms

$11.06 + 7.56 = 18.62$

So, the equation becomes:

$18.62 - 8.4x = 9.38$

Step 3: Subtract 18.62 from both sides

$-8.4x = -9.24$

Step 4: Divide both sides by -8.4

$x = \frac{-9.24}{-8.4}$

$x = 1.1$

This is another possible solution to the equation.

Conclusion

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Introduction

In our previous article, we explored the possible steps involved in solving the equation $3.5 + 1.2(6.3 - 7x) = 9.38$. We discussed three options for solving this equation and provided a step-by-step guide for each approach. In this article, we will answer some frequently asked questions about solving linear equations.

Q: What is the order of operations?

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

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate 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 distribute a coefficient to a term?

A: To distribute a coefficient to a term, you multiply the coefficient by each term inside the parentheses. For example, if we have the expression $2(3x + 4)$, we would distribute the 2 to both terms inside the parentheses:

$2(3x + 4) = 6x + 8$

Q: What is the difference between combining like terms and distributing a coefficient?

A: Combining like terms involves adding or subtracting terms that have the same variable and coefficient. For example, if we have the expression $3x + 2x$, we can combine the like terms:

$3x + 2x = 5x$

Distributing a coefficient, on the other hand, involves multiplying the coefficient by each term inside the parentheses. For example, if we have the expression $2(3x + 4)$, we would distribute the 2 to both terms inside the parentheses:

$2(3x + 4) = 6x + 8$

Q: How do I solve a linear equation with multiple variables?

A: To solve a linear equation with multiple variables, you need to isolate one variable on one side of the equation. You can do this by using inverse operations, such as addition, subtraction, multiplication, and division. For example, if we have the equation $2x + 3y = 5$, we can isolate the variable x by subtracting 3y from both sides:

$2x = 5 - 3y$

Then, we can divide both sides by 2 to solve for x:

$x = \frac{5 - 3y}{2}$

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 graph a linear equation?

A: To graph a linear equation, you need to find two points on the line and plot them on a coordinate plane. You can do this by substituting values for the variable into the equation and solving for the corresponding value of the other variable. For example, if we have the equation $y = 2x + 3$, we can find two points on the line by substituting x = 0 and x = 1 into the equation:

When x = 0, y = 2(0) + 3 = 3

When x = 1, y = 2(1) + 3 = 5

We can plot these two points on a coordinate plane and draw a line through them to represent the equation.

Conclusion

In this article, we answered some frequently asked questions about solving linear equations. We discussed the order of operations, distributing coefficients, combining like terms, solving linear equations with multiple variables, and graphing linear equations. By following these steps and understanding the concepts, you can become proficient in solving linear equations and apply them to real-world problems.