How do you evaluate 6[ x - ( x - 3x ) + 1] = 4x - 6?

1 Answer
Mar 6, 2018

x=-6/7

Explanation:

start by looking combining like terms in the inside parentheses.

6[x-(color(red)(x-3x))+1]=4x-6
6[x-(color(red)(-2x))+1]=4x-6

we can remove the parentheses because there's only one number inside them. also, subtracting a negative number is the same as adding. so we can rewrite the equation as:

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

now, we can combine like terms inside those parentheses

6[color(red)(x+2x)+1]=4x-6
6[color(red)(3x)+1]=4x-6

then distribute the 6 by multiplying each term inside the parentheses by 6

color(red)(6)[3x+1]=4x-6
color(red)(18x+6)=4x-6

subtract 4x from both sides of the equation to get all the x's on the same side, and combine like terms
18xcolor(red)(-4x)+6=4xcolor(red)(-4x)-6
14x+6=-6

subtract 6 from both sides to get the x's alone
14x+6color(red)(-6)=-6color(red)(-6)
14x=-12

divide by 14 to get x alone
(14x)/color(red)(14)=-12/color(red)(14)
x=-6/7