Question

How do you solve `52v - 68v + 76v - 66v + - 16v - - 9= 53`?

Answer 1

`v=-2`

Explanation:

Simplify:

`52v-68v+76v-66v-16v+9=53`

Subtract `9` from both sides

`52v-68v+76v-66v-16vcancel(+9color(red)(-9))=53color(red)(-9)`

`52v-68v+76v-66v-16v=44`

Combine the terms in the left side:

`-22v=44`

Divide `-22` from both sides

`cancel(-22)/cancel(color(red)(-22))v=44/color(red)(-22)`

`v=-2`

Answer 2

Combine the terms with variables, then solve.
`v = -2`

Explanation:

Any term with a similar variable can be combined with the normal rules of algebra. In this case it is just a series of additions and subtractions. It may be simplified by using the distributive property to show the distribution of the variable over the numbers.

`52v - 68v + 76v - 66v + (-16v) - (-9) = 53`
`52v - 68v + 76v - 66v - 16v + 9 = 53`

`52v - 68v + 76v - 66v - 16v = 53 - 9 = 44`

`v xx (52 - 68 + 76 - 66 - 16) = 44`

`v xx (- 22) = 44` ; `v = 44/(-22) = -2`

CHECK!:
`52(-2) - 68(-2) + 76(-2) - 66(-2) - 16(-2) + 9 = 53`
`-104 + 136 - 152 + 132 + 32 + 9 = 53`

`53 = 53` Correct!