Solve for v.

–19.6v − 2.65 + 2.3v = 4.91 − 16.7v


To solve for \( v \) in the equation 

\[ -19.6v - 2.65 + 2.3v = 4.91 - 16.7v \]

we will follow these steps:

1. Combine like terms involving \( v \) on the left-hand side of the equation.
2. Combine like terms involving \( v \) on the right-hand side of the equation.
3. Isolate \( v \) by moving all terms involving \( v \) to one side of the equation and constants to the other side.

Let's solve it step-by-step:

1. Combine like terms on the left-hand side:

\[ -19.6v + 2.3v - 2.65 = 4.91 - 16.7v \]

\[ (-19.6 + 2.3)v - 2.65 = 4.91 - 16.7v \]

\[ -17.3v - 2.65 = 4.91 - 16.7v \]

2. Combine like terms on the right-hand side:

There are no like terms to combine on the right-hand side, so we move on to isolating \( v \).

3. Move all terms involving \( v \) to one side and constants to the other:

Add \( 16.7v \) to both sides:

\[ -17.3v + 16.7v - 2.65 = 4.91 \]

\[ (-17.3 + 16.7)v - 2.65 = 4.91 \]

\[ -0.6v - 2.65 = 4.91 \]

Add \( 2.65 \) to both sides to isolate terms with \( v \):

\[ -0.6v = 4.91 + 2.65 \]

\[ -0.6v = 7.56 \]

4. Solve for \( v \):

Divide both sides by \(-0.6\):

\[ v = \frac{7.56}{-0.6} \]

\[ v = -12.6 \]

Thus, the solution is:

\[ v = -12.6 \]

Would you like more details or have any questions about this solution?

Here are some related questions to expand your understanding:

1. How do you solve linear equations with variables on both sides?
2. What are like terms, and how do you combine them?
3. How can you check your solution to an equation?
4. What are some common mistakes to avoid when solving equations?
5. How do you solve equations with fractions or decimals?
6. What are the steps to isolate the variable in an equation?
7. How do you solve an equation involving absolute values?
8. What strategies can be used to solve multi-step equations?

**Tip:** Always double-check your solution by substituting it back into the original equation to ensure it satisfies both sides.

Learn how to solve the linear equation -19.6v - 2.65 + 2.3v = 4.91 - 16.7v step-by-step with a detailed solution. This problem involves combining like terms, isolating the variable, and basic algebraic operations. Suitable for students in Grades 7-9.

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