Question

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

Answer 1

See the solution process below:

Explanation:

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

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

`4 - (color(red)(2) * 2) - (color(red)(2) * 4x) = x - 3`

`4 - 4 - 8x = x - 3`

`0 - 8x = x - 3`

`-8x = x - 3`

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

`-color(red)(x) - 8x = -color(red)(x) + x - 3`

`-1color(red)(x) - 8x = 0 - 3`

`(-1 - 8)x = -3`

`-9x = -3`

Now, divide each side of the equation by `color(red)(-9)` to solve for `x` while keeping the equation balanced:

`(-9x)/color(red)(-9) = (-3)/color(red)(-9)`

`(color(red)(cancel(color(black)(-9)))x)/cancel(color(red)(-9)) = (-3 xx 1)/color(red)(-3 xx 3)`

`x = (color(red)(cancel(color(black)(-3))) xx 1)/color(red)(color(black)(cancel(color(red)(-3))) xx 3)`

`x = 1/3`

Answer 2

`x=1/3`

Explanation:

Firstly, distribute the bracket.

`rArrcancel(4)cancel(-4)-8x=x-3`

`"subtract x from both sides"`

`-8x-x=cancel(x)cancel(-x)-3`

`rArr-9x=-3`

`"divide both sides by - 9"`

`(cancel(-9) x)/cancel(-9)=(-3)/(-9)`

`rArrx=1/3`

`color(blue)"As a check"`

Substitute this value into the equation and if the left side equals the right side then it is the solution.

`4-2(2+4/3)=4-2(10/3)=4-20/3=-8/3`

`1/3-3=1/3-9/3=-8/3larrcolor(red)" right side"`

`rArrx=1/3" is the solution"`