Question

$$\frac{x-1}{3}+4<\frac{x-5}{5}-2$$

Answer 1

$$\frac{x-1}{3}+4<\frac{x-5}{5}-2$$
$$\Rightarrow \frac{x-1}{3}-\frac{x-5}{5}<-2-4\left[\text{ Transposing 4 to the RHS and frac{x - 5}{5} to the LHS }\right]$$
$$\Rightarrow \frac{5(x-1)-3(x-5)}{15}<-6$$
$$\Rightarrow \frac{5x-5-3x+15}{15}<-6$$
$$\Rightarrow \frac{2x+10}{15}<-6$$
$$\Rightarrow 2x+10<-90$$
$$\Rightarrow 2x<-90-10\left[\text{ Transposing 10 to the RHS }\right]$$
$$\Rightarrow 2x<-100$$
$$\Rightarrow x<-\frac{100}{2}\left[\text{ Dividing both the sides by 2 }\right]$$
$$\Rightarrow x<-50$$
$$\text{ Hence, the solution of the given inequation is }(-\mathrm{\infty },-50).$$