How do you solve #4x + 2( 8- 3x ) = 12x#?

Question

Hazel Anglin · Accepted Answer

#x = 8/7#

Ok first you need to get the #x#'s on to one side and the numbers on their own on the over, so first expanding the bracket you get

#4x + 16 - 6x =12x#

After compiling similar terms, we have

#-2x +16 = 12x#

Now what we do to one side, we do to the other, so if we add #2x# to get rid of the #-2x#, we have to also add #2x# to the #12# so we end up with

#16=14x#

And supposedly you want just #x#, so we have to divide both sides by #14#, which is

#x = 16/14 = 8/7 ~~ 1.4286#

Isaiah Anthony · Answer

Simplify the expression, rearrange terms, and then solve to find #x=8/7#

Since the terms outside of the parentheses are divisible by two, I decided to divide both sides by two instead of multiplying the two terms inside the parentheses by the coefficient (2). This way, we can start by simplifying:

#(4x+2(8-3x))/2=(12x)/2#

#2x+(8-3x)=6x#

#2x+8-3x=6x#

We'll then combine similar terms:

#8+x(2-3)=6x#

#8-x=6x#

Next, we rearrange by adding #x# to both sides:

#8cancel(-x)color(red)(cancel(+x))=6xcolor(red)(+x)#

#8=x(6+color(red)(1))#

#8=7x#

Finally, we divide through by #x#'s coefficient:

#8/color(red)(7)=(cancel(7)x)/color(red)(cancel(7))#

#color(green)(x=8/7~=1.1429#

Hazel Anglin · Answer

undefined To solve the equation 4x + 2(8 - 3x) = 12x:

1. Distribute the 2 across the parentheses: 4x + 16 - 6x = 12x
2. Combine like terms: 4x - 6x + 16 = 12x
3. Combine x terms: -2x + 16 = 12x
4. Move 12x to the left side by subtracting it from both sides: -14x + 16 = 0
5. Move 16 to the right side by subtracting it from both sides: -14x = -16
6. Solve for x by dividing both sides by -14: x = (-16) / (-14)
7. Simplify: x = 8/7