Question

How do you solve `2(2x-5)=6x+4`?

Answer 1

See a solution process below:

Explanation:

First, expand the terms on the left side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(2)(2x - 5) = 6x + 4`

`(color(red)(2) xx 2x) - (color(red)(2) xx 5) = 6x + 4`

`4x - 10 = 6x + 4`

Next, subtract `color(red)(4x)` and `color(blue)(4)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-color(red)(4x) + 4x - 10 - color(blue)(4) = -color(red)(4x) + 6x + 4 - color(blue)(4)`

`0 - 14 = (-color(red)(4) + 6)x + 0`

`-14 = 2x`

Now, divide each side of the equation by `color(red)(2)` to solve for `x` while keeping the equation balanced:

`-14/color(red)(2) = (2x)/color(red)(2)`

`-7 = (color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2))`

`-7 = x`

`x = -7`

Answer 2

`x = -7`

Explanation:

First expand the brackets by multiplying each thing inside the brackets by 2:

`4x - 10 = 6x + 4`

then minus the `4x` so there are only `x`'s on one side:

`- 10 = 2x + 4`

then minus the `4` so there are only numbers on one side and `x`'s on the other:

`-14 = 2x`

then divide by `2` to get the value of `x`:

`-7 = x`