Question
i need help solving these inequalities i'm not sure if i should factor things out or not
4x^3 is greater than or equal to 16x
and
4 is greater than or equal to 2x^3 + 8x
4x^3 is greater than or equal to 16x
and
4 is greater than or equal to 2x^3 + 8x
Answers
MathMate
Yes, you can factor out <i>numbers</i> which are positive as in equations.
4x>16 can be written as
x>4
(common factor 4 is positive.)
If the factor is negative, you can still factor it out, <i>but</i> you will need to reverse the sign of inequality.
-5x ≥ 40
x ≤ 40/(-5)
x ≤ -8
(common factor -5 is negative)
If the sign of the factor is unknown, then you'll have to make different cases:
ax > ab
x > b (if a>0)
x < b (if a<0)
x is undefined if a=0
4x>16 can be written as
x>4
(common factor 4 is positive.)
If the factor is negative, you can still factor it out, <i>but</i> you will need to reverse the sign of inequality.
-5x ≥ 40
x ≤ 40/(-5)
x ≤ -8
(common factor -5 is negative)
If the sign of the factor is unknown, then you'll have to make different cases:
ax > ab
x > b (if a>0)
x < b (if a<0)
x is undefined if a=0
Francis
-y-4+2y>11