Question

How do you solve `234= 7( 6v + 2) + 2v`?

Answer 1

See a solution process below:

Explanation:

First, expand the term in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis:

`234 = color(red)(7)(6v + 2) + 2v`

`234 = (color(red)(7) xx 6v) + (color(red)(7) xx 2) + 2v`

`234 = 42v + 14 + 2v`

Next, group and combine like terms on the right side of the equation:

`234 = 42v + 2v + 14`

`234 = (42 + 2)v + 14`

`234 = 44v + 14`

Then, subtract `color(red)(14)` from each side of the equation to isolate the `v` term while keeping the equation balanced:

`234 - color(red)(14) = 44v + 14 - color(red)(14)`

`220 = 44v + 0`

`220 = 44v`

Now, divide each side of the equation by `color(red)(44)` to solve for `v` while keeping the equation balanced:

`220/color(red)(44) = (44v)/color(red)(44)`

`5 = (color(red)(cancel(color(black)(44)))v)/cancel(color(red)(44))`

`5 = v`

`v = 5`