Identify the values or range of values of x or y in the problems below. Write your answer in Inequality and interval notation

Question

Identify the values or range of values of x or y in the problems below. Write your answer in Inequality and interval notation

5. What are the values of x in 6x - 4y ≤ 24, when -1<y<6?

6.Whatarethevaluesofy inx+7y> 21,when 2<x≤9?

please help me answer this

Answer 1

a) 6x -4y is less than or = 24

divide by 2

3x -4y is less than or = 12

x </= 4 +4y/3

as y varies from -1 to 6

x varies from 2 2/3 to 12

x is in the interval [8/3, 12]

8/3 </= x </= 12

b) lnx + 7y > 21, what is y as x varies from more than 2 to 9??

7y > 21-lnx

y > 3 - (lnx)/7

y varies from more than 3 -(ln2)/7 to 3-(ln9)/7

3 - (ln2)/7 < y </= 3-(ln9)/7

y is in the interval

[3 -(ln2)/7, 3-(ln9)/7]