Question

Solve the following inequation and represent the solution on the number line:

3m – 5 ≤ 2m + 1, m is an integer

Answer 1

3m – 5 ≤ 2m + 1

Subtracting 1 on both the sides

3m – 5 – 1 ≤ 2m + 1 – 1

3m – 6 ≤ 2m

Subtracting 2m on both the sides

3m – 6 – 2m ≤ 2m – 2m

m – 6 ≤ 0

Adding 6 on both the sides

m – 6 + 6 ≤ 0 + 6

m ≤ 6

Since the solution belongs to the set of integers, the solution is 6, 5, 4, 3, 2, 1, 0, –1, … 

Its graph on number line is shown below