Question

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

Answer 1

`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`