**Question 6:**

List all the integer values of

*x*which satisfy the following linear inequalities:

–2 < 3

*x*+ 1 ≤ 10

**–2 < 3**

*Solution:*

*x*+ 1

–3 < 3

*x*

*x*> –1

*x*= 0, 1, 2, 3, …

3

*x*+ 1 ≤ 10

3

*x*≤ 9

*x*≤ 3

*x*= 3, 2, 1, 0, …

Therefore

*x*= 0, 1, 2, 3**Question 7:**

List all the integer values of

*x*which satisfy the following linear inequalities:

–5 < 2

*x*– 3 ≤ 1

**–5 < 2**

*Solution:*

*x*– 3

–5 + 3 < 2

*x*

2

*x*> –2

*x*> –1

*x*= 0, 1, 2, 3, …

2

*x*– 3 ≤ 1

2

*x*≤ 4

*x*≤ 2

*x*= 2, 1, 0, –1, …

Therefore

*x*= 0, 1, 2**Question 8:**

$\text{Giventhat}3\sqrt{x-2}4\text{and}x\text{isaninteger}\text{.Listallthepossiblevaluesof}x\text{.}$

Solution:Solution:

$\begin{array}{l}3<\sqrt{x-2}<4\\ {3}^{2}<x-2<{4}^{2}\\ 9<x-2\\ x>11\text{}\\ \\ \text{or}x-216\\ x18\\ \\ 11x18\\ x=12,\text{}13,\text{}14,\text{}15,\text{}16,\text{}17\end{array}$

**Question 9:**

Find the biggest and the smallest integer of

*x*that satisfy

3

*x*+ 2 ≥ –4 and 4 –

*x*> 0.

**3**

Solution:

Solution:

*x*+ 2 ≥ –4

3

*x*≥ –4 – 2

3

*x*≥ –6

*x*≥ –2

4 –

*x*> 0

–

*x*> –4

*x*< 4

Smallest integer of

*x*is –2, and the biggest integer of

*x*is 3.

**Question 10:**

$\begin{array}{l}\text{If}x\le h\le y\text{satisfythetwoinequalities}7-\frac{h}{2}\le 5\text{and}\\ 3\left(h+2\right)\le 20+h,\text{findthevaluesof}x\text{and}y.\end{array}$

Solution:Solution:

$\begin{array}{l}7-\frac{h}{2}\le 5\\ -\frac{h}{2}\le 5-7\\ -h\le -4\\ h\ge 4\\ \\ 3\left(h+2\right)\le 20+h\\ 3h+6\le 20+h\\ 2h\le 14\\ h\le 7\\ \\ 4\le h\le 7\\ \therefore x=4,y=7\end{array}$