Question

The solution set of:- x/2 - 5 ≤ x/3 – 4, where x= positive odd number

Answer 1

Explanation:

Given inequation is

2x+5≤3x+6 

⇒2(x+10)≤3(x+18)[Taking L.C.M on both sides]

⇒3(x+10)≤2(x+18) [On cross-multiplying]

⇒3x+30≤2x+36

⇒3x−2x≤36−30

⇒x≤6

As x is a positive odd integer.

Hence, the solution set is {1,3,5}.

(ii) Given inequation is , 

3(2x+3)≥4(3x–1)

⇒4(2x+3)≥3(3x–1) [On cross-multiplying]

⇒8x+12≥9x−3

⇒−9x+8x≥−12−3

⇒−x≥−15

⇒x≤15

As x is positive even integer.

Hence, the solution set is {2,4,6,8,10,12,14}.

Answer 2

Explanation:

Given inequation is

2x+5≤3x+6 

⇒2(x+10)≤3(x+18)[Taking L.C.M on both sides]

⇒3(x+10)≤2(x+18) [On cross-multiplying]

⇒3x+30≤2x+36

⇒3x−2x≤36−30

⇒x≤6

As x is a positive odd integer.

Hence, the solution set is {1,3,5}.

(ii) Given inequation is , 

3(2x+3)≥4(3x–1)

⇒4(2x+3)≥3(3x–1) [On cross-multiplying]

⇒8x+12≥9x−3

⇒−9x+8x≥−12−3

⇒−x≥−15

⇒x≤15

As x is positive even integer.

Hence, the solution set is {2,4,6,8,10,12,14}.

Answer 3

Explanation:

Given inequation is

2x+5≤3x+6 

⇒2(x+10)≤3(x+18)[Taking L.C.M on both sides]

⇒3(x+10)≤2(x+18) [On cross-multiplying]

⇒3x+30≤2x+36

⇒3x−2x≤36−30

⇒x≤6

As x is a positive odd integer.

Hence, the solution set is {1,3,5}.

(ii) Given inequation is , 

3(2x+3)≥4(3x–1)

⇒4(2x+3)≥3(3x–1) [On cross-multiplying]

⇒8x+12≥9x−3

⇒−9x+8x≥−12−3

⇒−x≥−15

⇒x≤15

As x is positive even integer.

Hence, the solution set is {2,4,6,8,10,12,14}.