-6 < -4x - 6 < 46
The object is to solve for x in the middle:
Add 6 to all three sides:
-6 + 6 < -4x - 6 + 6 < 46 + 6
0 < -4x < 52
Divide all three sides by -4. We must reverse the inequality
symbols when (and only when) we divide (or multiply) through
by a negative number. -4 is negative so we must reverse
the inequality symbols from < to > :
> >
0 > x > -13
That's the solution. That can also be written as
-13 < x < 0.
The solution SET can be indicated by a number line graph:
----------o===================================================o--------
-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2
or by set-builder notation:
{ x | -13 < x < 0 }
or by interval notation:
(-13, 0)
Edwin
