Question

Solve the inequation $2x-3\ge 5$ and find the minimum value of $x$. Also, represent the solution set on the number line.

Answer 1

Step 1: Solve the inequation

$$\begin{gathered} \Rightarrow 2x-3\ge 5 \\ \Rightarrow 2x\ge 5+3 \\ \Rightarrow x\ge \frac{8}{2} \\ \Rightarrow x\ge 4 \end{gathered}$$

Hence, the required solution set is $x\in [4,\infty )$ and the minimum value of $x$ is $4$.

Step 2: Represent the solution set on a number line

Thus, the required solution set is $\mathbf{x}\mathbf{\in }\mathbf{[}\mathbf{4}\mathbf{,}\mathbf{\infty }\mathbf{)}$ and the minimum value of $\mathit{x}$ is $\mathbf{4}$.