(a) n is an integer.

−2 < n ≤ 3

List the possible values of n.

Then solve;
Solve 3y − 4 > 17

The possible integer values of n are:

-1, 0, 1 , 2 , and 3.

-1 to 3 are all greater than -2.

3 is the maximum since 3 is the greatest number where n is equal to it or lesser than it.

Solving the inequality: 3y - 4 > 17

3y - 4 > 17

Add 4 to both sides to move it.

3y > 17 + 4

3y > 21

Divide both sides by 3 to get the value of y.

3y/3 > 21

y > 7

The sign does not change since we did not divide or multiply by a negative.

Therefore, y is greater than 7.

Inequality given:

Interval notation:

Writing down the values of

The set (N) for possible values of is:

Now, solving the inequality

Interval notation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47