Question

(a) n is an integer.

Answer 1

Answer:

$n \in \mathbb{Z}$

Inequality given:

$-2 < n \leq 3$

Interval notation: $(-2, 3]$

$\{n \in \mathbb{Z}| -2$

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: $(7, \infty)$

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

Answer 2

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.