Question

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

Answer 1

`\large\boxed{x>3\to x\in(3,\ \infty)}`

Explanation:

`3(8-4x)<6(x-5)\qquad\text{use distributive property}\\\\(3)(8)+(3)(-4x)<(6)(x)+(6)(-5)\\\\24-12x<6x-30\qquad\text{subtract 24 from both sides}\\\\-12x<6x-54\qquad\text{subtract 6x from both sides}\\\\-18x<-54\qquad\text{change the signs}\\\\18x>54\qquad\text{divide both sides by 18}\\\\x>3`