What Is The Value Of $r$ In The Equation? − 15 ( 4 − R ) = − 12 -15(4-r)=-12 − 15 ( 4 − R ) = − 12 A. − 6 -6 − 6 B. − 4 -4 − 4 C. 4 4 4
Introduction
In algebra, solving for the value of a variable in a linear equation is a fundamental concept. It involves isolating the variable on one side of the equation and finding its value. In this article, we will solve for the value of r in the equation -15(4-r) = -12.
Understanding the Equation
The given equation is -15(4-r) = -12. To solve for r, we need to isolate the variable r on one side of the equation. The equation involves a negative sign, parentheses, and a variable r. We will use the distributive property to simplify the equation and solve for r.
Step 1: Distribute the Negative Sign
The first step is to distribute the negative sign to the terms inside the parentheses. This will change the sign of each term inside the parentheses.
-15(4-r) = -15(4) + 15r
Step 2: Simplify the Equation
Now, we simplify the equation by evaluating the expression -15(4).
-15(4) = -60
So, the equation becomes:
-60 + 15r = -12
Step 3: Isolate the Variable r
To isolate the variable r, we need to get rid of the constant term -60 on the left side of the equation. We can do this by adding 60 to both sides of the equation.
-60 + 60 + 15r = -12 + 60
This simplifies to:
15r = 48
Step 4: Solve for r
Now, we can solve for r by dividing both sides of the equation by 15.
15r / 15 = 48 / 15
This simplifies to:
r = 48 / 15
Simplifying the Fraction
To simplify the fraction, we can divide both the numerator and the denominator by their greatest common divisor, which is 3.
r = (48 / 3) / (15 / 3)
This simplifies to:
r = 16 / 5
Conclusion
In this article, we solved for the value of r in the equation -15(4-r) = -12. We used the distributive property to simplify the equation, isolated the variable r, and solved for its value. The final answer is r = 16/5, which is equivalent to 3.2.
Answer
The correct answer is:
- A. is incorrect
- B. is incorrect
- C. is incorrect
- The correct answer is not listed, but the solution is
Frequently Asked Questions (FAQs) about Solving for r in a Linear Equation ====================================================================
Q: What is the first step in solving for r in the equation -15(4-r) = -12?
A: The first step is to distribute the negative sign to the terms inside the parentheses. This will change the sign of each term inside the parentheses.
Q: How do I simplify the equation after distributing the negative sign?
A: After distributing the negative sign, you will have the equation -60 + 15r = -12. To simplify the equation, you can evaluate the expression -15(4) and replace it with -60.
Q: How do I isolate the variable r in the equation?
A: To isolate the variable r, you need to get rid of the constant term -60 on the left side of the equation. You can do this by adding 60 to both sides of the equation.
Q: What is the next step after isolating the variable r?
A: After isolating the variable r, you will have the equation 15r = 48. To solve for r, you need to divide both sides of the equation by 15.
Q: How do I simplify the fraction 48/15?
A: To simplify the fraction 48/15, you can divide both the numerator and the denominator by their greatest common divisor, which is 3.
Q: What is the final answer for the value of r in the equation -15(4-r) = -12?
A: The final answer for the value of r in the equation -15(4-r) = -12 is r = 16/5, which is equivalent to 3.2.
Q: What if I get a different answer for the value of r?
A: If you get a different answer for the value of r, it may be due to a mistake in the calculation. Make sure to double-check your work and follow the steps outlined in the solution.
Q: Can I use a calculator to solve for r in the equation?
A: Yes, you can use a calculator to solve for r in the equation. However, make sure to follow the steps outlined in the solution and check your work to ensure accuracy.
Q: What is the importance of solving for r in a linear equation?
A: Solving for r in a linear equation is an important concept in algebra. It helps you understand how to isolate variables and solve for their values, which is a fundamental skill in mathematics.
Q: Can I apply the steps outlined in the solution to other linear equations?
A: Yes, you can apply the steps outlined in the solution to other linear equations. The steps are general and can be used to solve for variables in a wide range of linear equations.
Q: What if I'm still having trouble solving for r in a linear equation?
A: If you're still having trouble solving for r in a linear equation, it may be helpful to seek additional help from a teacher, tutor, or online resource.