Solve For $c$.$2+\frac{7}{c}=\frac{3}{5}$Simplify Your Answer As Much As Possible.
Introduction
In this article, we will delve into the world of algebra and focus on solving for the variable c in the given equation 2 + 7/c = 3/5. This equation involves fractions and a variable in the denominator, making it a bit more complex than a standard linear equation. We will use algebraic techniques to isolate the variable c and simplify the expression.
Understanding the Equation
The given equation is 2 + 7/c = 3/5. To solve for c, we need to isolate the variable c on one side of the equation. The first step is to get rid of the fraction 7/c by multiplying both sides of the equation by c. This will eliminate the fraction and make it easier to work with.
Multiplying Both Sides by c
Multiplying both sides of the equation by c gives us:
2c + 7 = 3c/5
Eliminating the Fraction
To eliminate the fraction 3c/5, we can multiply both sides of the equation by 5. This will get rid of the fraction and make it easier to work with.
Multiplying both sides by 5 gives us:
10c + 35 = 3c
Isolating the Variable c
Now that we have eliminated the fraction, we can focus on isolating the variable c. To do this, we need to get all the terms involving c on one side of the equation. We can do this by subtracting 3c from both sides of the equation.
Subtracting 3c from both sides gives us:
7c + 35 = 0
Solving for c
Now that we have isolated the variable c, we can solve for its value. To do this, we need to get rid of the constant term 35. We can do this by subtracting 35 from both sides of the equation.
Subtracting 35 from both sides gives us:
7c = -35
Dividing Both Sides by 7
To solve for c, we need to divide both sides of the equation by 7. This will give us the value of c.
Dividing both sides by 7 gives us:
c = -35/7
Simplifying the Expression
The expression -35/7 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 7.
Simplifying the expression gives us:
c = -5
Conclusion
In this article, we have solved for the variable c in the equation 2 + 7/c = 3/5. We used algebraic techniques to isolate the variable c and simplify the expression. The final value of c is -5.
Tips and Tricks
- When solving equations with fractions, it's often helpful to multiply both sides of the equation by the denominator to eliminate the fraction.
- When isolating a variable, make sure to get all the terms involving the variable on one side of the equation.
- When simplifying expressions, look for common factors in the numerator and denominator that can be divided out.
Frequently Asked Questions
- Q: What is the value of c in the equation 2 + 7/c = 3/5? A: The value of c is -5.
- Q: How do I solve for c in an equation with a fraction? A: To solve for c, multiply both sides of the equation by the denominator to eliminate the fraction, then isolate the variable c.
- Q: What is the greatest common divisor of 35 and 7?
A: The greatest common divisor of 35 and 7 is 7.
Introduction
In our previous article, we solved for the variable c in the equation 2 + 7/c = 3/5. We used algebraic techniques to isolate the variable c and simplify the expression. In this article, we will answer some frequently asked questions related to solving for c in the equation 2 + 7/c = 3/5.
Q&A
Q: What is the value of c in the equation 2 + 7/c = 3/5?
A: The value of c is -5.
Q: How do I solve for c in an equation with a fraction?
A: To solve for c, multiply both sides of the equation by the denominator to eliminate the fraction, then isolate the variable c.
Q: What is the greatest common divisor of 35 and 7?
A: The greatest common divisor of 35 and 7 is 7.
Q: Why do I need to multiply both sides of the equation by c to eliminate the fraction?
A: You need to multiply both sides of the equation by c to eliminate the fraction because the fraction 7/c is multiplied by c on the left-hand side of the equation. This will cancel out the fraction and make it easier to work with.
Q: How do I know which side of the equation to add or subtract from?
A: When solving for c, you need to add or subtract from the side of the equation that has the variable c. In this case, we added 3c to both sides of the equation to get all the terms involving c on one side.
Q: What if the equation has multiple variables?
A: If the equation has multiple variables, you need to isolate one variable at a time. Start by isolating the variable that is easiest to work with, then move on to the other variables.
Q: Can I use a calculator to solve for c?
A: Yes, you can use a calculator to solve for c. However, make sure to check your work by plugging the value of c back into the original equation to ensure that it is true.
Q: What if I get stuck while solving for c?
A: If you get stuck while solving for c, try breaking down the problem into smaller steps. Write down the equation and the steps you have taken so far, then try to identify the next step. If you are still stuck, try asking a friend or a teacher for help.
Tips and Tricks
- When solving equations with fractions, it's often helpful to multiply both sides of the equation by the denominator to eliminate the fraction.
- When isolating a variable, make sure to get all the terms involving the variable on one side of the equation.
- When simplifying expressions, look for common factors in the numerator and denominator that can be divided out.
- Use a calculator to check your work and ensure that the value of c is correct.
Conclusion
Solving for c in the equation 2 + 7/c = 3/5 requires careful attention to detail and a step-by-step approach. By following the steps outlined in this article, you can solve for c and simplify the expression. Remember to check your work and use a calculator to ensure that the value of c is correct.
Frequently Asked Questions
- Q: What is the value of c in the equation 2 + 7/c = 3/5? A: The value of c is -5.
- Q: How do I solve for c in an equation with a fraction? A: To solve for c, multiply both sides of the equation by the denominator to eliminate the fraction, then isolate the variable c.
- Q: What is the greatest common divisor of 35 and 7? A: The greatest common divisor of 35 and 7 is 7.
Additional Resources
- For more information on solving equations with fractions, see our article on "Solving Equations with Fractions".
- For more information on algebraic techniques, see our article on "Algebraic Techniques for Solving Equations".
- For more information on simplifying expressions, see our article on "Simplifying Expressions".