Question

Describe two different ways to solve the inequality $3(a+5)<9$.

Answer 1

Step 1 : Solving the inequality

Given inequality: $3(a+5)<9$
$$\begin{gathered} \Rightarrow a+5<\frac{9}{3} \\ \Rightarrow a+5<3 \end{gathered}$$ [ Divide both sides by $3$ ]
$\Rightarrow a+5–5<3–5$ [ Subtract $5$ from both sides ]
$\therefore a<-2$

Step 2 : Solving the inequality by a different way.

First, expand the given inequality, we get;
$$\begin{gathered} 3(a+5)<9 \\ \Rightarrow 3a+15<9 \end{gathered}$$
$\Rightarrow 3a-15<9–15$ [ Subtract $15$ from both sides ]
$\Rightarrow 3a<-6$
$\Rightarrow \frac{3a}{3}<\frac{-6}{3}$ [ Divide both sides by $3$]
$\therefore a<-2$

Hence, two different ways to solve the inequality $3(a+5)<9$ are described above whose solution is $a<-2$.