Solve For $c$.$\frac{c}{0.6} + 1.6 = -0.9$

Solving for $c$ in the Equation $\frac{c}{0.6} + 1.6 = -0.9$

Understanding the Problem

The given equation is $\frac{c}{0.6} + 1.6 = -0.9$. Our goal is to solve for the variable $c$. This equation involves a fraction and a constant term, and we need to isolate the variable $c$ to find its value.

Breaking Down the Equation

To solve for $c$, we need to isolate the term involving $c$ on one side of the equation. The equation can be broken down into two main parts: the fraction $\frac{c}{0.6}$ and the constant term $1.6$. We can start by subtracting $1.6$ from both sides of the equation to get rid of the constant term.

Subtracting 1.6 from Both Sides

$\frac{c}{0.6} + 1.6 - 1.6 = -0.9 - 1.6$

This simplifies to:

$\frac{c}{0.6} = -2.5$

Multiplying Both Sides by 0.6

To get rid of the fraction, we can multiply both sides of the equation by $0.6$. This will give us:

$c = -2.5 \times 0.6$

Evaluating the Expression

$c = -1.5$

Therefore, the value of $c$ is $-1.5$.

Checking the Solution

To verify our solution, we can plug in the value of $c$ back into the original equation and check if it holds true.

$\frac{-1.5}{0.6} + 1.6 = -2.5 + 1.6$

This simplifies to:

$-2.5 + 1.6 = -0.9$

Since the equation holds true, our solution is correct.

Conclusion

In this article, we solved for the variable $c$ in the equation $\frac{c}{0.6} + 1.6 = -0.9$. We broke down the equation into two main parts, subtracted $1.6$ from both sides, multiplied both sides by $0.6$, and evaluated the expression to find the value of $c$. Our solution was verified by plugging in the value of $c$ back into the original equation.
Solving for $c$ in the Equation $\frac{c}{0.6} + 1.6 = -0.9$: Q&A

Frequently Asked Questions

We've solved for the variable $c$ in the equation $\frac{c}{0.6} + 1.6 = -0.9$, but you may still have some questions. Here are some frequently asked questions and their answers.

Q: What is the first step in solving for $c$?

A: The first step in solving for $c$ is to subtract $1.6$ from both sides of the equation to get rid of the constant term.

Q: Why do we multiply both sides by $0.6$?

A: We multiply both sides by $0.6$ to get rid of the fraction. This is a common technique used to eliminate fractions in equations.

Q: How do we verify our solution?

A: We verify our solution by plugging in the value of $c$ back into the original equation and checking if it holds true.

Q: What if the equation had a different constant term?

A: If the equation had a different constant term, we would simply subtract that term from both sides of the equation and then proceed with the rest of the solution.

Q: Can we use this technique to solve other equations with fractions?

A: Yes, this technique can be used to solve other equations with fractions. The key is to identify the fraction and eliminate it by multiplying both sides by the denominator.

Q: What if the equation had a different denominator?

A: If the equation had a different denominator, we would simply multiply both sides by that denominator to eliminate the fraction.

Q: How do we know if our solution is correct?

A: We know if our solution is correct by verifying it by plugging in the value of $c$ back into the original equation and checking if it holds true.

Common Mistakes to Avoid

When solving for $c$ in the equation $\frac{c}{0.6} + 1.6 = -0.9$, there are a few common mistakes to avoid.

Mistake 1: Not subtracting $1.6$ from both sides

If we don't subtract $1.6$ from both sides, we'll be left with an equation that still has a fraction.

Mistake 2: Not multiplying both sides by $0.6$

If we don't multiply both sides by $0.6$, we'll still have a fraction in the equation.

Mistake 3: Not verifying the solution

If we don't verify our solution by plugging in the value of $c$ back into the original equation, we may end up with an incorrect solution.

Conclusion

Solving for $c$ in the equation $\frac{c}{0.6} + 1.6 = -0.9$ requires careful attention to detail and a clear understanding of the steps involved. By following the steps outlined in this article and avoiding common mistakes, you can confidently solve for $c$ and verify your solution.