Consider the equation $\frac{5}{3} v+4+\frac{1}{3} v=8$. What is the resulting equation after the first step in the solution?
$\frac{5}{3} v+4=8-\frac{1}{3} v$
$\frac{4}{3} v+4=8$
$4+v=8-\frac{5}{3} v$
$2 v+4=8$
Answer (1)
Combine the terms with 'v': 3 5 v + 3 1 v = 2 v .
Substitute the combined term back into the original equation: 2 v + 4 = 8 .
The resulting equation after the first step is 2 v + 4 = 8 .
Explanation
Analyze the problem We are given the equation 3 5 v + 4 + 3 1 v = 8 and asked to find the resulting equation after the first step in the solution. The first step would be to combine like terms, specifically the terms with the variable v .
Combine like terms We combine the terms with v : 3 5 v + 3 1 v . To do this, we add the coefficients since they have a common denominator: 3 5 + 3 1 = 3 5 + 1 = 3 6 = 2 So, 3 5 v + 3 1 v = 2 v .
Write the resulting equation Now we substitute this back into the original equation: 2 v + 4 = 8 This is the resulting equation after the first step.
State the final answer Therefore, the resulting equation after the first step in the solution is 2 v + 4 = 8 .
Examples
In physics, this type of equation could represent a force balance problem where 'v' is a velocity. Combining terms is like simplifying the forces acting in the same direction to make the problem easier to solve. For example, if you have two forces acting on an object in the same direction, you would add them together to find the net force. This is a fundamental concept in mechanics and is used to solve a wide variety of problems.
