1. ## Signed 6

In solving
-7x + x = 24 -x

x = - 4

Where do we get the 6?

-7x + x = 24 - x + x somehow this line produces a six for -6x = 24

In solving
-7x + x = 24 -x

x = - 4

Where do we get the 6?

-7x + x = 24 - x + x somehow this line produces a six for -6x = 24
-7x + x = -6x

since we started with -7x's and we added one x to it, so we have one more than -7x's now, which is -6x

this is wrong however, you should add x to both sides:

$\displaystyle -7x + x = 24 - x$

$\displaystyle \Rightarrow -7x + x + x = 24 - x + x$ ......add x to both sides

$\displaystyle \Rightarrow -5x = 24$

$\displaystyle \Rightarrow x = - \frac {24}{5}$

3. So, one more than -7x's equals 6x instead of eight x?

-7x = 24 -x

-7x = 24 + -1x

-7x + x = 24 + -1x + x

-7x + x = somehow equals -6x instead of eight x.

-6x = 24 + -1x + x

-1x + x = 0

-6x = 24 + 0

-6x = 24

x = -4

So, one more than -7x's equals 6x instead of eight x?

-7x = 24 -x

-7x = 24 + -1x

-7x + x = 24 + -1x + x

-7x + x = somehow equals -6x instead of eight x.

-6x = 24 + -1x + x

-1x + x = 0

-6x = 24 + 0

-6x = 24

x = -4
so the original equation was $\displaystyle -7x = 24 - x$?

ok. obviously you're having trouble adding -7 and + 1

-7 + 1 = -6, not 8. if you can't see this, rearrange it, put the +1 in front. we get:

1 - 7 = ? obviously the answer isn't 8! it's -6

if you still don't see it, draw it on a number line. if you start at the point labeled -7 and move 1 unit in the positive direction, you will end up at -6

$\displaystyle -7x = 24 - x$

$\displaystyle \Rightarrow -7x + x = 24 - x + x$

$\displaystyle \Rightarrow x - 7x = 24$

$\displaystyle \Rightarrow -6x = 24$

$\displaystyle \Rightarrow x = - \frac {24}{6}$

$\displaystyle \Rightarrow x = -4$