Question

Which of the following equations results in no solutions?

Answer 1

A. This gives us 3v + 15 = 3v - 4. This is no solutions because the slope is the same and the y-intercept is different.

Answer 2

Answer:

$\boxed{\sf A) \:3(v + 5) = 2v - 4 + v}$

Step-by-step explanation:

$\sf A )\:3(v + 5) = 2v - 4 + v$

Combine like terms:

$\sf 3\left(v+5\right)=3v-4$

Expand:

$\sf 3v+15=3v-4$

Subtract 15 from both sides:

$\sf 3v+15-15=3v-4-15$

$\sf 3v=3v-19$

Subtract 3v from both sides:

$\sf 3v-3v=3v-19-3v$

$\sf 0=-19$

$\boxed{\sf{No\:Solution}}$

_________________

$\sf B )\:3(v + 5) = 2v + 15 + v$

Combine like terms:

$\sf 3\left(v+5\right)=3v+15$

Expand:

$\sf 3v+15=3v+15$

Subtract 15 from both sides:

$\sf 3v+15-15=3v+15-15$

$\sf 3v=3v$

Subtract 3v from both sides:

$\boxed{\sf 0=0}$

_______________________

$\sf C)\: 3(v + 5) = 2v + 15$

Expand:

$\sf 3v+15=2v+15$

Subtract 15 from both sides:

$\sf 3v=2v$

Subtract 2v from both sides:

$\sf 3v-2v=2v-2v$

$\boxed{\sf v=0}$

_______________________

$\sf D)\: 3(v + 5) = 2v - 4$

Expand:

$\sf 3v+15=2v-4$

Subtract 15 from both sides:

$\sf 3v+15-15=2v-4-15$

$\sf 3v=2v-19$

Subtract 2v from both sides:

$\sf 3v-2v=2v-19-2v$

$\boxed{\sf v=-19}$

___________________________