Question

solve for v.
\\(\frac{3v}{v + 6} = \frac{7v}{v + 6} + 4\\)
if there is more than one solution, separate them with commas.
if there is no solution, click on
o solution\.
\\(v = \\)

Explanation:

Step1: Eliminate denominators

Multiply all terms by $v+6$ ($v
eq -6$):
$3v = 7v + 4(v+6)$

Step2: Expand the right-hand side

Distribute the 4 across $v+6$:
$3v = 7v + 4v + 24$

Step3: Combine like terms

Sum the $v$-terms on the right:
$3v = 11v + 24$

Step4: Isolate $v$-terms on one side

Subtract $11v$ from both sides:
$3v - 11v = 24$
$-8v = 24$

Step5: Solve for $v$

Divide both sides by $-8$:
$v = \frac{24}{-8} = -3$

Step6: Verify the solution

Check that $v=-3$ does not make the original denominator zero: $-3 + 6 = 3
eq 0$, so it is valid.

Answer:

$-3$