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Which of the following equations results in no solutions?
A 3(v + 5) = 2v - 4 + v
B 3(v + 5) = 2v + 15 + v
C 3(v + 5) = 2v + 15
D 3(v + 5) = 2v - 4

Sagot :

Answer:

[tex]\boxed{\sf A) \:3(v + 5) = 2v - 4 + v}[/tex]

Step-by-step explanation:

[tex]\sf A )\:3(v + 5) = 2v - 4 + v[/tex]

Combine like terms:

[tex]\sf 3\left(v+5\right)=3v-4[/tex]

Expand:

[tex]\sf 3v+15=3v-4[/tex]

Subtract 15 from both sides:

[tex]\sf 3v+15-15=3v-4-15[/tex]

[tex]\sf 3v=3v-19[/tex]

Subtract 3v from both sides:

[tex]\sf 3v-3v=3v-19-3v[/tex]

[tex]\sf 0=-19[/tex]

[tex]\boxed{\sf{No\:Solution}}[/tex]

_________________

[tex]\sf B )\:3(v + 5) = 2v + 15 + v[/tex]

Combine like terms:

[tex]\sf 3\left(v+5\right)=3v+15[/tex]

Expand:

[tex]\sf 3v+15=3v+15[/tex]

Subtract 15 from both sides:

[tex]\sf 3v+15-15=3v+15-15[/tex]

[tex]\sf 3v=3v[/tex]

Subtract 3v from both sides:

[tex]\boxed{\sf 0=0}[/tex]

_______________________

[tex]\sf C)\: 3(v + 5) = 2v + 15[/tex]

Expand:

[tex]\sf 3v+15=2v+15[/tex]

Subtract 15 from both sides:

[tex]\sf 3v=2v[/tex]

Subtract 2v from both sides:

[tex]\sf 3v-2v=2v-2v[/tex]

[tex]\boxed{\sf v=0}[/tex]

_______________________

[tex]\sf D)\: 3(v + 5) = 2v - 4[/tex]

Expand:

[tex]\sf 3v+15=2v-4[/tex]

Subtract 15 from both sides:

[tex]\sf 3v+15-15=2v-4-15[/tex]

[tex]\sf 3v=2v-19[/tex]

Subtract 2v from both sides:

[tex]\sf 3v-2v=2v-19-2v[/tex]

[tex]\boxed{\sf v=-19}[/tex]

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