Question
Solve and graph the solution set on a number line : $\frac{2 \mathrm{x}}{5}+1<-3 ; \mathrm{x} \in \mathrm{R}$
✓
Answer
$\frac{2 \mathrm{x}}{5}+1<-3$
$ \Rightarrow \frac{2 \mathrm{x}}{5}+1-1<-3-1 \ ($Subtracting from both sides$)$
$ \Rightarrow \frac{2 \mathrm{x}}{5}<-4$
$ \Rightarrow \frac{2 \mathrm{x}}{5} \times 5<-4 \times 5 \ldots ($Multiplying both sides by $5)$
$ \Rightarrow 2 \mathrm{x}<-20$
$ \Rightarrow \frac{2 \mathrm{x}}{2}<\frac{-20}{2} \ldots ($Dividing both sides by $2)$
$ \Rightarrow \mathrm{x}<-10$
$\therefore$ The required graph is :
$ \Rightarrow \frac{2 \mathrm{x}}{5}+1-1<-3-1 \ ($Subtracting from both sides$)$
$ \Rightarrow \frac{2 \mathrm{x}}{5}<-4$
$ \Rightarrow \frac{2 \mathrm{x}}{5} \times 5<-4 \times 5 \ldots ($Multiplying both sides by $5)$
$ \Rightarrow 2 \mathrm{x}<-20$
$ \Rightarrow \frac{2 \mathrm{x}}{2}<\frac{-20}{2} \ldots ($Dividing both sides by $2)$
$ \Rightarrow \mathrm{x}<-10$
$\therefore$ The required graph is :
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