Solve The Linear Equation:$\[ 3.4 + 2(9.7 - 4.8x) = 61.2 \\]What Are The Possible Steps Involved In Solving The Equation? Check All That Apply.- Distribute 2 To 9.7 And \[$-4.8x\$\].- Combine 3.4 And 19.4.- Divide Both Sides By

**Solving Linear Equations: A Step-by-Step Guide** =====================================================

What is a Linear Equation?

A linear equation is an algebraic equation in which the highest power of the variable(s) is 1. It is a simple equation that can be solved using basic algebraic operations. Linear equations are used to model real-world problems and are a fundamental concept in mathematics.

The Equation: $3.4 + 2(9.7 - 4.8x) = 61.2$

To solve this equation, we need to follow a series of steps. Let's break it down:

Step 1: Distribute 2 to 9.7 and $-4.8x$

When we see a number or variable inside parentheses, we need to multiply it by the number or variable outside the parentheses. In this case, we need to distribute 2 to both 9.7 and $-4.8x$.

2(9.7 - 4.8x) = 2(9.7) - 2(4.8x)

This simplifies to:

19.4 - 9.6x

So, the equation becomes:

3.4 + 19.4 - 9.6x = 61.2

Step 2: Combine 3.4 and 19.4

Now, we can combine the constants on the left-hand side of the equation.

3.4 + 19.4 = 22.8

So, the equation becomes:

22.8 - 9.6x = 61.2

Step 3: Subtract 22.8 from both sides

To isolate the term with the variable, we need to subtract 22.8 from both sides of the equation.

-9.6x = 61.2 - 22.8

This simplifies to:

-9.6x = 38.4

Step 4: Divide both sides by -9.6

Finally, we can solve for x by dividing both sides of the equation by -9.6.

x = -38.4 / 9.6

This simplifies to:

x = -4

Q&A

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

A: The first step in solving a linear equation is to distribute any numbers or variables outside the parentheses to the terms inside the parentheses.

Q: Can we combine constants on the left-hand side of the equation?

A: Yes, we can combine constants on the left-hand side of the equation by adding or subtracting them.

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

A: The final step in solving a linear equation is to divide both sides of the equation by the coefficient of the variable.

Q: What is the solution to the equation $3.4 + 2(9.7 - 4.8x) = 61.2$?

A: The solution to the equation $3.4 + 2(9.7 - 4.8x) = 61.2$ is x = -4.

Q: Can we solve a linear equation by adding or subtracting the same value to both sides?

A: No, we cannot solve a linear equation by adding or subtracting the same value to both sides. This is not a valid algebraic operation.

Q: What is the purpose of solving a linear equation?

A: The purpose of solving a linear equation is to find the value of the variable that makes the equation true. This is useful in a variety of real-world applications, such as solving problems in physics, engineering, and economics.

Conclusion

Solving linear equations is a fundamental concept in mathematics that has numerous real-world applications. By following the steps outlined in this article, you can solve linear equations and find the value of the variable that makes the equation true. Remember to distribute numbers or variables outside the parentheses, combine constants on the left-hand side of the equation, and divide both sides of the equation by the coefficient of the variable. With practice and patience, you can become proficient in solving linear equations and apply this skill to a variety of problems.