m1v1 + m2v2=(m1+m2)v3 find m1

If you could please explain it too or show the steps I would appreciate it.

Assume all other variables are known.

m1v1 + m2v2=(m1+m2)v3
expand each side:
m1v1 + m2v2= m1v3 + m2v3
group terms containing m1 on the left, others on the right
m1v1-m1v3 = m2v3 - m2v2
Factorize m1 and m2
m1(v1-v3) = m2(v3-v2)
Divide by the coefficient of m1:
m1 = m2(v3-v2)/(v1-v3)

To find m1 in the equation m1v1 + m2v2 = (m1 + m2)v3, you need to rearrange the equation to isolate m1 on one side.

Step 1: Distribute the v3 term on the right side of the equation:

m1v1 + m2v2 = m1v3 + m2v3

Step 2: Bring all the terms with m1 on one side by subtracting m1v3 from both sides of the equation:

m1v1 - m1v3 + m2v2 = m2v3

Step 3: Factor out m1:

m1(v1 - v3) + m2v2 = m2v3

Step 4: Subtract m2v2 from both sides of the equation:

m1(v1 - v3) = m2v3 - m2v2

Step 5: Divide both sides of the equation by (v1 - v3) to solve for m1:

m1 = (m2v3 - m2v2) / (v1 - v3)

So, the value of m1 can be calculated using the expression (m2v3 - m2v2) / (v1 - v3).

To solve the equation m1v1 + m2v2 = (m1 + m2)v3 for m1, we can follow these steps:

Step 1: Expand the equation
m1v1 + m2v2 = m1v3 + m2v3

Step 2: Rearrange the equation
m1v1 - m1v3 = m2v3 - m2v2

Step 3: Factor out m1 on the left side
m1(v1 - v3) = m2(v3 - v2)

Step 4: Divide both sides of the equation by (v1 - v3) to isolate m1
m1 = (m2(v3 - v2))/(v1 - v3)

So, the solution for m1 is (m2(v3 - v2))/(v1 - v3).