Question

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Answer 1

3(8-4x) < 6(x-5)
24 -12x < 6x -30
24 +30 < 6x +12x
54 < 18x

54/18 < x

3 < x 

so the number line which represents the solution set for given inequality started with 3 but is greater than 3 and go away till plus infinity 

hope this will help you 

Answer 2

Answer:

The number line which represents the solution set for inequality 3(8-4x)<6(x-5) is $(3,\infty)$

Step-by-step explanation:

Given an inequality 3(8-4x)<6(x-5).

We have to find the solution set for the given inequality.

$3(8-4x)<6(x-5)$

⇒ $24-12x<6x-30$

⇒ $24+30<6x+12x$

⇒ $54<18x$

⇒ $x>\frac{54}{18}$

⇒ $x>3$

Hence, the number line which represents the solution set for inequality 3(8-4x)<6(x-5) is $(3,\infty)$ i.e start from 3 and goes up to infinity.