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
Understanding the Equation
When solving a linear equation, it's essential to follow a specific order of operations to ensure that the equation is simplified correctly. The given equation is:
This equation involves a combination of addition, multiplication, and subtraction. To solve it, we need to follow the correct order of operations.
Step 1: Distribute the Coefficient
The first step in solving this equation is to distribute the coefficient 1.2 to the terms inside the parentheses. This means that we need to multiply 1.2 by each term inside the parentheses.
By distributing the coefficient, we have simplified the equation and made it easier to work with.
Step 2: Combine Like Terms
The next step is to combine like terms. In this equation, we have two like terms: 3.5 and 1.2(6.3). We can combine these terms by adding them together.
By combining like terms, we have further simplified the equation.
Step 3: Simplify the Equation
Now that we have combined like terms, we can simplify the equation by evaluating the expression 3.5 + 7.56.
By simplifying the equation, we have made it easier to solve.
Step 4: Isolate the Variable
The final step is to isolate the variable x. To do this, we need to get rid of the constant term on the left-hand side of the equation.
By isolating the variable, we have set up the equation to solve for x.
Step 5: Solve for x
The final step is to solve for x. To do this, we need to get rid of the coefficient 1.2 that is being multiplied by the variable x.
By solving for x, we have found the value of the variable.
Conclusion
In conclusion, solving a linear equation involves a series of steps, including distributing the coefficient, combining like terms, simplifying the equation, isolating the variable, and solving for x. By following these steps, we can solve even the most complex linear equations.
Answer Options
Based on the steps outlined above, the correct answer options are:
A. Add 3.5 and 1.2: This is not the correct answer, as we need to distribute the coefficient 1.2 to the terms inside the parentheses.
B. Distribute 1.2 to 6.3 and -7x: This is the correct answer, as we need to distribute the coefficient 1.2 to the terms inside the parentheses.
C. Combine 6.3 and -7x: This is not the correct answer, as we need to distribute the coefficient 1.2 to the terms inside the parentheses.
D. Combine 3.5: This is not the correct answer, as we need to distribute the coefficient 1.2 to the terms inside the parentheses.
Final Answer
Q: What is the first step in solving a linear equation?
A: The first step in solving a linear equation is to distribute the coefficient to the terms inside the parentheses. This means that you need to multiply the coefficient by each term inside the parentheses.
Q: What is the order of operations in solving a linear equation?
A: The order of operations in solving a linear equation is:
- Distribute the coefficient to the terms inside the parentheses.
- Combine like terms.
- Simplify the equation.
- Isolate the variable.
- Solve for x.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is an equation that can be written in the form ax + b = c, where a, b, and c are constants. A quadratic equation, on the other hand, is an equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants.
Q: How do I know if an equation is linear or quadratic?
A: To determine if an equation is linear or quadratic, you need to look at the highest power of the variable. If the highest power of the variable is 1, then the equation is linear. If the highest power of the variable is 2, then the equation is quadratic.
Q: What is the purpose of combining like terms in a linear equation?
A: The purpose of combining like terms in a linear equation is to simplify the equation and make it easier to solve. Like terms are terms that have the same variable and coefficient.
Q: How do I combine like terms in a linear equation?
A: To combine like terms in a linear equation, you need to add or subtract the coefficients of the like terms. For example, if you have the equation 2x + 3x, you can combine the like terms by adding the coefficients: 2x + 3x = 5x.
Q: What is the purpose of isolating the variable in a linear equation?
A: The purpose of isolating the variable in a linear equation is to get the variable by itself on one side of the equation. This makes it easier to solve for the variable.
Q: How do I isolate the variable in a linear equation?
A: To isolate the variable in a linear equation, you need to get rid of the constant term on the same side of the equation as the variable. You can do this by adding or subtracting the same value to both sides of the equation.
Q: What is the final step in solving a linear equation?
A: The final step in solving a linear equation is to solve for the variable. This means that you need to find the value of the variable that makes the equation true.
Q: How do I solve for the variable in a linear equation?
A: To solve for the variable in a linear equation, you need to isolate the variable and then divide both sides of the equation by the coefficient of the variable.
Q: What are some common mistakes to avoid when solving linear equations?
A: Some common mistakes to avoid when solving linear equations include:
- Not distributing the coefficient to the terms inside the parentheses.
- Not combining like terms.
- Not isolating the variable.
- Not solving for the variable.
- Making errors when adding or subtracting numbers.
Q: How can I practice solving linear equations?
A: You can practice solving linear equations by working through examples and exercises in a textbook or online resource. You can also try solving linear equations on your own by creating your own problems and solutions.
Q: What are some real-world applications of linear equations?
A: Linear equations have many real-world applications, including:
- Modeling population growth and decline.
- Calculating the cost of goods and services.
- Determining the amount of time it takes to complete a task.
- Finding the area and perimeter of shapes.
- Solving problems in physics and engineering.
Conclusion
In conclusion, solving linear equations is an essential skill that has many real-world applications. By following the steps outlined in this guide, you can learn how to solve linear equations and apply them to a variety of problems. Remember to practice regularly and avoid common mistakes to become proficient in solving linear equations.