Question

(a) n is an integer.

−2 < n ≤ 3

List the possible values of n.

Then solve;
Solve 3y − 4 > 17

Answer 1

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.

Answer 2

`n \in \mathbb{Z}`

Inequality given:

`-2 < n \leq 3`

Interval notation:
`(-2, 3]`

`\{n \in \mathbb{Z}| -2<n\leq 3 \}`

Writing down the values of
`n`

The set (N) for possible values of
`n` is:

`N=\{-1, 0, 1, 2, 3\}`

Now, solving the inequality
`3y - 4 > 17`

`3y - 4 > 17\\3y-4+4>17+4\\3y>21\\y>7`

Interval notation:
`(7, \infty)`

`\{n \in \mathbb{R}| y>7 \}`