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
$\displaystyle \Rightarrow -5x = 24$
$\displaystyle \Rightarrow x = - \frac {24}{5}$
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
$\displaystyle -7x = 24 - x$
$\displaystyle \Rightarrow -7x + x = 24 - x + x$
$\displaystyle \Rightarrow x - 7x = 24$
$\displaystyle \Rightarrow -6x = 24$
$\displaystyle \Rightarrow x = - \frac {24}{6}$
$\displaystyle \Rightarrow x = -4$