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
