How do you solve 4/5z < -1/3?

It's just like an ordinary equation:

4/5z < -1/3

Cross-multiply

-5z < 12

Divide everything by -5 to get z by itself (also, don't forget to switch the signs because you're dividing by a negative number):

z > 12/-5
z > -0.24

4/(5z) < -1/3, Is this what you want?
4/(5z) + 1/3 < 0
(12+5z)/15 < 0
12+5z < 0
z > -12/5
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Ideas: Collect all terms in one side first.

we consider two cases.

first,if z=0, then it's impossible to solve the inequality.

second, if z is not zero, then, by multiplying z to both sides, we have
4/5<-z/3
multiplying both side by 3, we have
12/5<-z
multplying both sides by -1, we have
-12/5>z **(multiplying by a negative number we change < by >, for example, 3<5 but -3>-5)
or equvalently, z< -12/5

Take 3 to the left and 5z to the right.
12<-5z
Multiply by -1 on both sides and simultaneously change the < to >. (that is a rule for solving)
So, -12>5z
Take 5 to the left.
-12/5>z
z<-12/5

My answer assumes that you have the z on the numerator and not the denominator.

(4/5)z < -1/3
4z < -5/3 (by multiplying both sides by 5)
z < -5/12 (dividing both sides by 4).

just solve like a regular equation

solve for z by dividing -1/3 by 4/5
z < (-1/3)/(4/5) Note that -1/3 divided by 4/5 is the same thing as multiplying -1/3 by the recriprocal, 5/4
z < -5/12

Side Note: just a rule with these kinds of problems...if you ever divide by a negative you switch the sign from < to > or > to <. Hope that helped!

the 1st step, do away with the pesky fractions by potential of multiplying the two factors by potential of 12. We get 3(2x - 3) < 4(3x + a million) Now distribute 6x - 9 < 12x + 4 Now simplify -13 < 6x Now divide by potential of 6 -13/6 < x

Assume you mean :-
(4/5) z < - 1/3
4 z < - 5/3
z < - 5/12
PS
You MUST use brackets to clarify question.
You will note the confusion you have caused amongst answerers by not using brackets.

you treat the < just as if it were an equal sign and multiply both sides by 5/4 so z < -5/12 is ur anwser.... make sure to reverse the direction of the < when multiplying both sides by negative numbers (not in this case)

4/5z < -1/3
4 < -5z/3
12 < -5z
-5z > 12
z < -12/5 (-2.4)