Question

How do you solve `4(x-9)-3(-x+2)=14`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Be careful to handle the signs for each term correctly:

`color(red)(4)(x - 9) - color(blue)(3)(-x + 2) = 14`

`(color(red)(4) xx x) - (color(red)(4) xx 9) - (color(blue)(3) xx -x) - (color(blue)(3) xx 2) = 14`

`4x - 36 - (-3x) - 6 = 14`

`4x - 36 + 3x - 6 = 14`

Next, group and combine like terms:

`4x + 3x - 36 - 6 = 14`

`(4 + 3)x + (-36 - 6) = 14`

`7x + (-42) = 14`

`7x - 42 = 14`

Then, add `color(red)(42)` to each side of the equation to isolate the `x` term while keeping the equation balanced:

`7x - 42 + color(red)(42) = 14 + color(red)(42)`

`7x - 0 = 56`

`7x = 56`

Now, divide each side of the equation by `color(red)(7)` to solve for `x` while keeping the equation balanced:

`(7x)/color(red)(7) = 56/color(red)(7)`

`(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = 8`

`x = 8`