6y − 5 ≤ 2y + 7
6y − 2y − 5 ≤ 2y − 2y + 7 [Subtracting 2y from both sides]
4y − 5 ≤ 7
4y − 5 + 5 ≤ 7 + 5 [Adding 5 on both sides]
4y ≤ 12
\(\cfrac { 4y }{ 4 } \le \cfrac { 12 }{ 4 } \) [Dividing by 4 on both sides]
y ≤ 3
Since the solution belongs to integers, the solutions are 3, 2, 1, 0, –1, –2,..... It’s graph on the number line is shown below.

−2 ≤ z + 3 ≤ 5
−2 −3 ≤ z + 3 −3 ≤ 5 −3 [Subtracting −3 from the inequation]
−5 ≤ z ≤ 2
Since the solution belongs to integers, the solutions are –5, –4 , –3, –2, –1, 0, 1 and 2. It’s graph on the number line is shown below:

Let the number of workers be x.
Then, the wages that x workers will earn per day = Rs.200x
The wages that x workers will earn per month = Rs.(200x x 30) = Rs.6000x
Given that, this amount cannot exceed Rs.300000.
Otherwise, it can be written as 6000 x ≤ 300000
\(\frac {6000x}{6000 } \le \frac {300000 }{6000 } \) 
\(x\le 50\) 
Thus, up to 50 workers can be employed on a monthly budget of Rs.300000.

5 − 7x ≥ 33
5 − 5 − 7x ≥ 33 − 5 [Subtracting 5 from both sides]
−7x ≥ 28
\(\cfrac { -7x }{ -7 } \ge \cfrac { 28 }{ 7 } \)  [Dividing both sides by –7]
\(x\le -4\) [since, it is divided by a negative number, the inequality is reversed]
Since, solution belongs to the set of integers, that are less than −4, we take the values of x as –4, –5, –6, ...
Therefore, the solutions are –4, –5, –6,...

2x + 4 < 18
2x + 4 – 4 < 18 − 4 [Subtracting 4 from both sides]
2x < 14 [Divide by 2 on both sides]
x < 7
Since the solution belongs to natural numbers, that are less than 7, we take the values of the x as 1, 2, 3, 4, 5 and 6.
Therefore, the solutions are 1, 2, 3, 4, 5 and 6.