Question

How do you solve `4(x-1)-2(3x+5)=-3x-1`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the two terms within parenthesis on the left side of the equation:

`color(red)(4)(x - 1) - color(blue)(2)(3x + 5) = -3x - 1`

`(color(red)(4) xx x) - (color(red)(4) xx 1) - (color(blue)(2) xx 3x) - (color(blue)(2) xx 5) = -3x - 1`

`4x - 4 - 6x - 10 = -3x - 1`

Next, combine like terms on the left side of the equation:

`4x - 6x - 4 - 10 = -3x - 1`

`(4 - 6)x - 14 = -3x - 1`

`-2x - 14 = -3x - 1`

Now, add `color(red)(3x)` and `color(blue)(14)` to each side of the equation to solve for `x` while keeping the equation balanced:

`-2x - 14 + color(red)(3x) + color(blue)(14) = -3x - 1 + color(red)(3x) + color(blue)(14)`

`-2x + color(red)(3x) - 14 + color(blue)(14) = -3x + color(red)(3x) - 1 + color(blue)(14)`

`(-2 + 3)x - 0 = 0 + 13`

`1x = 13`

`x = 13`