Simplify The Expression. Write Your Answer Using Integers Or Improper Fractions. \frac{1}{2} V - 3\left(-3v - \frac{3}{2}\right ]Answer: □ \square □

Understanding the Problem

The given expression is $\frac{1}{2} v - 3\left(-3v - \frac{3}{2}\right)$. Our goal is to simplify this expression and write the answer using integers or improper fractions.

Step 1: Distribute the Negative Sign

The first step is to distribute the negative sign inside the parentheses. This will change the sign of each term inside the parentheses.

$\frac{1}{2} v - 3\left(-3v - \frac{3}{2}\right) = \frac{1}{2} v - 3(-3v) - 3\left(-\frac{3}{2}\right)$

Step 2: Simplify the Terms

Now, let's simplify each term inside the expression.

$\frac{1}{2} v - 3(-3v) - 3\left(-\frac{3}{2}\right) = \frac{1}{2} v + 9v + \frac{9}{2}$

Step 3: Combine Like Terms

Next, we need to combine like terms. In this case, we have two terms with the variable $v$ and one term with a constant.

$\frac{1}{2} v + 9v + \frac{9}{2} = \left(\frac{1}{2} + 9\right)v + \frac{9}{2}$

Step 4: Simplify the Coefficient

Now, let's simplify the coefficient of the variable $v$.

$\left(\frac{1}{2} + 9\right)v + \frac{9}{2} = \left(\frac{1}{2} + \frac{18}{2}\right)v + \frac{9}{2}$

Step 5: Combine the Fractions

Finally, let's combine the fractions.

$\left(\frac{1}{2} + \frac{18}{2}\right)v + \frac{9}{2} = \frac{19}{2}v + \frac{9}{2}$

Simplifying the Expression

To simplify the expression further, we can combine the two terms with the variable $v$.

$\frac{19}{2}v + \frac{9}{2} = \frac{19v + 9}{2}$

The Final Answer

Therefore, the simplified expression is $\boxed{\frac{19v + 9}{2}}$.

Conclusion

Understanding the Problem

The given expression is $\frac{1}{2} v - 3\left(-3v - \frac{3}{2}\right)$. Our goal is to simplify this expression and write the answer using integers or improper fractions.

Q: What is the first step in simplifying the expression?

A: The first step is to distribute the negative sign inside the parentheses. This will change the sign of each term inside the parentheses.

Q: How do I distribute the negative sign?

A: To distribute the negative sign, you need to change the sign of each term inside the parentheses. For example, if you have $-3(-3v - \frac{3}{2})$, you would change the sign of each term inside the parentheses to get $3(3v + \frac{3}{2})$.

Q: What is the next step in simplifying the expression?

A: The next step is to simplify each term inside the expression. This involves combining like terms and simplifying the coefficient.

Q: How do I simplify the terms?

A: To simplify the terms, you need to combine like terms and simplify the coefficient. For example, if you have $\frac{1}{2} v + 9v + \frac{9}{2}$, you would combine the like terms to get $\left(\frac{1}{2} + 9\right)v + \frac{9}{2}$.

Q: What is the final step in simplifying the expression?

A: The final step is to simplify the coefficient and combine the fractions. This will give you the final simplified expression.

Q: How do I simplify the coefficient?

A: To simplify the coefficient, you need to combine the fractions. For example, if you have $\left(\frac{1}{2} + \frac{18}{2}\right)v + \frac{9}{2}$, you would combine the fractions to get $\frac{19}{2}v + \frac{9}{2}$.

Q: What is the final simplified expression?

A: The final simplified expression is $\boxed{\frac{19v + 9}{2}}$.

Common Mistakes to Avoid

• Not distributing the negative sign correctly
• Not combining like terms correctly
• Not simplifying the coefficient correctly
• Not combining the fractions correctly

Tips and Tricks

• Make sure to distribute the negative sign correctly
• Combine like terms as soon as possible
• Simplify the coefficient as soon as possible
• Combine the fractions as soon as possible

Conclusion

Simplifying an expression involves a series of steps, including distributing the negative sign, simplifying the terms, combining like terms, and simplifying the coefficient. By following these steps and avoiding common mistakes, you can simplify complex expressions and write the answer using integers or improper fractions.