Question

How do you solve `4( 8+ 2x ) - 6( x + 3) = - 5x + 6x`?

Answer 1

`x = -14`

Explanation:

`4(8+2x) - 6(x+3) = -5x + 6x`

First, combine `-5x + 6x`:
`4(8+2x) - 6(x+3) = x`

Now use the distributive property (shown below) to expand/simplify `4(8+2x)` and `-6(x+3)`:

Following this image, we know that:
`color(blue)(4(8+2x) = (4 * 8) + (4 * 2x) = 32 + 8x)`
and
`color(blue)(-6(x+3) = (-6 * x) + (-6 * 3) = -6x - 18)`

Put them back into the equation:
`32 + 8x - 6x - 18 = x`

Combine like terms on the left side:
`14 + 2x = x`

Subtract `color(blue)(2x)` from both sides:
`14 + 2x quadcolor(blue)(-quad2x) = x quadcolor(blue)(-quad2x)`

`14 = -x`

Divide both sides by `color(blue)(-1)`:
`14/color(blue)(-1) = (-x)/color(blue)(-1)`

`-14 = x`

Therefore, `x = -14`.

Hope this helps!