Question 581129
{{{-8x+3>=27}}}
Adding (-3) to both sides (or subtracting 3 from both sides), the greater than or equal relationship is still true, so
{{{-8x>=27-3}}} --> {{{-8x>=24}}}
Multiplying (or dividing) both sides by a positive number maintains the inequality relationship, but multiplying (or dividing) both sides by a negative number reverses it. If we multiply both sides by {{{-1/8}}} (or divide both sides by {{{-8}}}),
{{{-8x>=24}}} transforms into the equivalent {{{((-8)/(-8))*x<=24/(-8)}}}
That {{{((-8)/(-8))}}} is optional, of course.
You could write {{{x<=24/(-8)}}} and no one should object.
Then you just do the {{{24/(-8)}}} division and end up with
{{{highlight(x<=-3)}}}
You can verify by seeing, for example, that x=-3, and x=-4 are solutions of the original inequality, but x=0 is not.
If multiplying by negative numbers when solving inequalities makes you nervous, you can go the long way around it, just adding stuff and only multiplying/dividing by positive numbers, like this
{{{-8x>=24}}} --> {{{-8x+8x>=24+8x}}} --> {{{0>=24+8x}}} --> {{{0-24>=24+8x-24}}} --> {{{-24>=8x}}} --> {{{-24/8>=8x/8}}} --> {{{-3>=x}}}