Write and solve the inequality that represents negative one eighth is less than the product of negative two thirds and a number.

A. negative one eighth is less than negative two thirds y where y is less than three sixteenths
B. negative one eighth is less than or equal to negative two thirds y where y is greater than negative three sixteenths
C. negative two thirds is less than negative one eighth y where y is less than one twelfth
D. negative two thirds is greater than negative one eighth y where y is greater than negative one twelfth



Answer :

Answer: The inequality represents "negative one eighth is less than the product of negative two thirds and a number". We can write this as:

-1/8 < (-2/3)y

To solve for y, we can multiply both sides by -3/2 to get rid of the fraction on the right side:

(-3/2)(-1/8) < y

This simplifies to:

3/16 < y

So, the correct answer is:

A. negative one eighth is less than negative two thirds y where y is greater than three sixteenths

Step-by-step explanation: I know wut I doin bru

Answer:

A. negative one eighth is less than negative two thirds y where y is less than three sixteenths

Step-by-step explanation:

Let y = the arbitrary number chosen in this inequality

Starting with the description:

Negative one-eighth < product of negative  two-thirds and y

[tex]\text{Negative = -}[/tex]
[tex]\text{Product = multiplication = *}[/tex]

gives us:

[tex]- \text{one eighth} < - \text{two-thirds} * y[/tex]

[tex]= > \:\:- \dfrac{1}{8} < -\dfrac{2}{3} * y[/tex]

Looking at the answer choices we can eliminate
B: has less-than-or-equal-to (≤) rather than <
D has is-greater-than (>)

C. can be eliminated since it reverses the items on either side of the < sign  and corresponds to [tex]- \dfrac{2}{3} < -\dfrac{1}{8}y[/tex]

Correct choice is A

If you wanted to verify the part where it says.. "y less than three sixteenths" proceed as follows

Original inequality:
[tex]\:\:- \dfrac{1}{8} < -\dfrac{2}{3} * y[/tex]

To find range of y:

Multiply both sides by -1 this reverses the signs and also the inequality direction

[tex](-1) * \left(-\dfrac{1}{8}\right) > (-1)*\left(-\dfrac{2}{3}\right) * y\\\\= > \dfrac{1}{8} > \dfrac{2}{3}y[/tex]

Multiply both sides by [tex]\dfrac{3}{2}[/tex]:
[tex]\dfrac{3}{2}*\dfrac{1}{8} > \dfrac{3}{2}* \dfrac{2}{3}y\\\\\dfrac{3}{16} > y[/tex]

This is equivalent to  
[tex]y < \dfrac{3}{16}[/tex]

This part corresponds to the last part of the statement in option A:
"where y is less than three sixteenths"

(because a> x is same as x < a)

Final Answer
Option A