Question

Solve for v: 5v + 23 = 6v + 4v - 17. Simplify your answer as much as possible.

Answer 1

To solve for v, combine like terms, then isolate variable terms on one side and constants on the other, resulting in the solution v = 8.

Step-by-step explanation:

To solve for v in the equation 5v + 23 = 6v + 4v - 17, we first simplify both sides of the equation. We combine like terms on the right side:

6v + 4v = 10v

So the equation now is:

5v + 23 = 10v - 17

Next, we want to get all terms containing v on one side and the constants on the other side. To do this, we subtract 5v from both sides:

23 = 10v - 5v - 17

Which simplifies to:

23 = 5v - 17

Adding 17 to both sides to isolate the variable term gives us:

23 + 17 = 5v

Which simplifies further to:

40 = 5v

Finally, we divide both sides of the equation by 5:

v = 40 / 5

v = 8

So, the solution is v = 8. We then check our solution to see if it is reasonable by substituting back into the original equation.

Answer 2

Simplified answer is v = 40

Step-by-step explanation:

To solve for v in the equation 5v + 23 = 6v + 4v - 17, first combine like terms on the right side:

5v + 23 = 10v - 17

Next, isolate v by subtracting 5v from both sides:

23 = 5v - 17

Finally, add 17 to both sides and divide by 5:

40 = v

Therefore, the solution is v = 40.

Understanding the steps involved in combining like terms and isolating variables is fundamental in algebra, providing a foundation for solving various equations and inequalities.