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

2 Answers
Sep 30, 2017

Answer:

#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"#

Sep 30, 2017

Answer:

#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#