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

2 Answers
Apr 26, 2017

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

Apr 26, 2017

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"