Question

How do you solve `6=2(-4+2x)-2(1+6x)` using the distributive property?

Answer 1

`x=-2`

Explanation:

`"distribute the brackets using the distributive property"`

`•color(white)(x)a(b+c)=ab+ac`

`rArr6=-8+4x-2-12x`

`rArr6=-10-8x`

`"add 10 to both sides"`

`6+10=cancel(-10)cancel(+10)-8x`

`rArr16=-8x`

`"divide both sides by "-8`

`16/(-8)=(cancel(-8) x)/cancel(-8)`

`rArrx=-2`

`color(blue)"As a check"`

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

`2(-4-4)-2(1-12)=(2xx-8)-(2xx-11)=-16+22=6`

`rArrx=-2" is the solution"`

Answer 2

`x = -2`

Explanation:

Question : `6=2(-4+2x)-2(1+6x)`

Distributive property :

`a(b -c) = ab - ac`

Let us apply the distributive property :

`2(-4+2x)` will give us `(2\times-4) + (2\times2x)`

and

`2(1+6x)` will give us `(2\times1) + (2\times6x)`

So, by the distributive property,

`[2(-4+2x)]-[2(1+6x)]=6`

can also be written as :

`[(2\times-4) + (2\times2x)] - [(2\times1) + (2\times6x)] = 6`

Multiplication :

`[(-8) + (4x)] - [(2)+(12x)] = 6`

Removing the Parenthesis :

`-8 +4x -2 -12x =6`

Grouping the like terms :

`(-8 -2) +(4x -12x) = 6`

`-10 - 8x = 6`

Transposition :

`-8x = 6 + 10`

`-8x = 16`

`-x = 16/8`

`-x = 2`

`x=-2`