Question

Are the inequalities $c+3>5$ and $c-1>1$ equivalent? Explain.

Answer 1

Step 1 : Solve the first inequality

We have,

$$\begin{gathered} \Rightarrow c+3>5 \\ \Rightarrow c>5-3[\mathrm{Transposing}3\mathrm{to}\mathrm{the}\mathrm{right}] \\ \therefore c>2 \end{gathered}$$

So, $c$ can take all the values which are greater than $2$.

Step 2 : Solve the second inequality

We have,

$$\begin{gathered} \Rightarrow c-1>1 \\ \Rightarrow c>1+1[\mathrm{Transposing}-1\mathrm{to}\mathrm{the}\mathrm{right}] \\ \therefore c>2 \end{gathered}$$

So, $c$ can take all the values which are greater than $2$.

Hence, both inequalities are equivalent.