How do you solve #12+5v=2v-9#?

Question

Nathan Axel · Accepted Answer

See a solution process below:

First, subtract #color(red)(12)# and #color(blue)(2v)# from each side of the equation to isolate the #v# term while keeping the equation balanced: #12 + 5v - color(red)(12) - color(blue)(2v) = 2v - 9 - color(red)(12) - color(blue)(2v)# #12 - color(red)(12) + 5v - color(blue)(2v) = 2v - color(blue)(2v) - 9 - color(red)(12)# #0 + (5 - color(blue)(2))v = 0 - 21# #3v = -21# Now, divide each side of the equation by #color(red)(3)# to solve for #y# while keeping the equation balanced: #(3v)/color(red)(3) = -21/color(red)(3)# #(color(red)(cancel(color(black)(3)))v)/cancel(color(red)(3)) = -7# #v = -7#

Nathan Axel · Answer

undefined To solve the equation 12 + 5v = 2v - 9, you first need to isolate the variable v. Subtract 2v from both sides to move all terms involving v to one side of the equation. This gives you 12 + 3v = -9. Then, subtract 12 from both sides to isolate the term with v. This results in 3v = -21. Finally, divide both sides by 3 to solve for v, yielding v = -7.

Hazel Anglin · Answer

undefined To solve the equation $12 + 5v = 2v - 9$, you first need to isolate the variable $v$ by performing operations to both sides of the equation to get $v$ by itself.

Here are the steps to solve it:

1. Subtract $2v$ from both sides:
$$ 12 + 5v - 2v = 2v - 2v - 9 $$
$$ 12 + 3v = -9 $$

2. Subtract 12 from both sides:
$$ 12 + 3v - 12 = -9 - 12 $$
$$ 3v = -21 $$

3. Divide both sides by 3:
$$ \frac{3v}{3} = \frac{-21}{3} $$
$$ v = -7 $$

So, the solution to the equation $12 + 5v = 2v - 9$ is $v = -7$.