Solve For $b$.$-4=\frac{b-9}{-2}$Find The Value Of $ B B B [/tex].
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Introduction
In algebra, solving for a variable means isolating that variable on one side of the equation. This is a crucial skill in mathematics, as it allows us to find the value of a variable and make predictions about real-world phenomena. In this article, we will focus on solving for the variable b in the equation -4 = (b-9)/(-2).
Understanding the Equation
The given equation is -4 = (b-9)/(-2). To solve for b, we need to isolate the variable b on one side of the equation. The first step is to understand the equation and identify the operations that need to be performed.
Multiplication and Division
The equation contains a fraction, which can be eliminated by multiplying both sides of the equation by the denominator. In this case, the denominator is -2. By multiplying both sides of the equation by -2, we can eliminate the fraction and make the equation easier to solve.
Step 1: Multiply Both Sides by -2
To eliminate the fraction, we multiply both sides of the equation by -2. This gives us:
-4 × (-2) = (b-9) × (-2)
Simplifying the Equation
Now that we have eliminated the fraction, we can simplify the equation by multiplying the numbers on both sides.
Step 3: Simplify the Equation
Multiplying -4 by -2 gives us 8. Multiplying (b-9) by -2 gives us -2b + 18. So, the simplified equation is:
8 = -2b + 18
Isolating the Variable
Now that we have simplified the equation, we can isolate the variable b by moving the constant term to the other side of the equation.
Step 4: Isolate the Variable
To isolate the variable b, we need to get rid of the constant term 18 on the right-hand side of the equation. We can do this by subtracting 18 from both sides of the equation.
8 - 18 = -2b + 18 - 18
Simplifying the Equation
Now that we have subtracted 18 from both sides of the equation, we can simplify the equation by combining the numbers on the left-hand side.
Step 5: Simplify the Equation
Subtracting 18 from 8 gives us -10. So, the simplified equation is:
-10 = -2b
Solving for b
Now that we have isolated the variable b, we can solve for b by dividing both sides of the equation by -2.
Step 6: Solve for b
To solve for b, we need to get rid of the coefficient -2 on the left-hand side of the equation. We can do this by dividing both sides of the equation by -2.
-10 ÷ (-2) = -2b ÷ (-2)
Simplifying the Equation
Now that we have divided both sides of the equation by -2, we can simplify the equation by combining the numbers on the right-hand side.
Step 7: Simplify the Equation
Dividing -10 by -2 gives us 5. So, the simplified equation is:
b = 5
Conclusion
In conclusion, we have solved for the variable b in the equation -4 = (b-9)/(-2). By following the steps outlined in this article, we have isolated the variable b and found its value to be 5.
Frequently Asked Questions
Q: What is the value of b in the equation -4 = (b-9)/(-2)?
A: The value of b is 5.
Q: How do I solve for b in an equation?
A: To solve for b, you need to isolate the variable b on one side of the equation. This can be done by performing operations such as multiplication, division, addition, and subtraction.
Q: What is the difference between solving for a variable and isolating a variable?
A: Solving for a variable means finding the value of that variable, while isolating a variable means getting that variable on one side of the equation.
Final Thoughts
Solving for a variable is an essential skill in mathematics, and it requires a deep understanding of algebraic operations and equations. By following the steps outlined in this article, you can solve for a variable and make predictions about real-world phenomena. Remember to always isolate the variable on one side of the equation and to perform operations in the correct order.
Additional Resources
For more information on solving for a variable, check out the following resources:
- Khan Academy: Solving Linear Equations
- Mathway: Solving for a Variable
- Algebra.com: Solving Linear Equations
References
- [1] "Algebra" by Michael Artin
- [2] "Linear Algebra and Its Applications" by Gilbert Strang
- [3] "Introduction to Algebra" by I.M. Gelfand
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Q&A: Solving for b
Q: What is the value of b in the equation -4 = (b-9)/(-2)?
A: The value of b is 5.
Q: How do I solve for b in an equation?
A: To solve for b, you need to isolate the variable b on one side of the equation. This can be done by performing operations such as multiplication, division, addition, and subtraction.
Q: What is the difference between solving for a variable and isolating a variable?
A: Solving for a variable means finding the value of that variable, while isolating a variable means getting that variable on one side of the equation.
Q: Can I use a calculator to solve for b?
A: Yes, you can use a calculator to solve for b. However, it's always a good idea to understand the steps involved in solving for a variable, as this will help you to check your work and ensure that you have the correct solution.
Q: How do I know if I have the correct solution?
A: To check your solution, you can plug the value of b back into the original equation and see if it is true. If the equation is true, then you have the correct solution.
Q: Can I use this method to solve for other variables?
A: Yes, this method can be used to solve for other variables. However, you will need to adjust the steps accordingly to suit the specific equation you are working with.
Q: What if I have a fraction in my equation?
A: If you have a fraction in your equation, you can eliminate it by multiplying both sides of the equation by the denominator.
Q: What if I have a negative number in my equation?
A: If you have a negative number in your equation, you can handle it by following the rules of arithmetic for negative numbers.
Q: Can I use this method to solve for variables in more complex equations?
A: Yes, this method can be used to solve for variables in more complex equations. However, you will need to adjust the steps accordingly to suit the specific equation you are working with.
Advanced Q&A
Q: How do I solve for b in an equation with multiple variables?
A: To solve for b in an equation with multiple variables, you will need to isolate the variable b on one side of the equation. This can be done by performing operations such as multiplication, division, addition, and subtraction.
Q: How do I solve for b in an equation with a quadratic expression?
A: To solve for b in an equation with a quadratic expression, you will need to isolate the variable b on one side of the equation. This can be done by performing operations such as multiplication, division, addition, and subtraction.
Q: How do I solve for b in an equation with a rational expression?
A: To solve for b in an equation with a rational expression, you will need to eliminate the fraction by multiplying both sides of the equation by the denominator.
Common Mistakes
Q: What is the most common mistake when solving for b?
A: The most common mistake when solving for b is to forget to isolate the variable b on one side of the equation.
Q: How can I avoid making this mistake?
A: To avoid making this mistake, you can make sure to follow the steps outlined in this article and to check your work carefully.
Q: What is the next most common mistake when solving for b?
A: The next most common mistake when solving for b is to make a mistake when performing operations such as multiplication, division, addition, and subtraction.
Q: How can I avoid making this mistake?
A: To avoid making this mistake, you can make sure to follow the rules of arithmetic and to check your work carefully.
Conclusion
Solving for b is an essential skill in mathematics, and it requires a deep understanding of algebraic operations and equations. By following the steps outlined in this article and by practicing regularly, you can become proficient in solving for b and tackle more complex equations with confidence.
Additional Resources
For more information on solving for b, check out the following resources:
- Khan Academy: Solving Linear Equations
- Mathway: Solving for a Variable
- Algebra.com: Solving Linear Equations
References
- [1] "Algebra" by Michael Artin
- [2] "Linear Algebra and Its Applications" by Gilbert Strang
- [3] "Introduction to Algebra" by I.M. Gelfand