Question

Solve the following inequation and represent the solution set on the number line: $\frac{2x+1}{2}+2(3-x)\le 7,\forall x\in R$

Answer 1

Step 1: Solve the given inequation to find the value of $x$.

$$\begin{gathered} \Rightarrow \frac{2x+1}{2}+2(3-x)\le 7 \\ \Rightarrow \frac{2x+1}{2}+6-2x\le 7 \\ \Rightarrow \frac{2x+1-4x}{2}\le 7-6 \\ \Rightarrow \frac{1-2x}{2}\le 1 \\ \Rightarrow 1-2x\le 2 \\ \Rightarrow 1-2\le 2x \\ \Rightarrow \frac{-1}{2}\le x \end{gathered}$$

Hence, the required solution set is $\{x:x\le \frac{-1}{2},x\in R\}$ .

Step 2: Using the solution set, represent the solution on number line

Thus, the required solution set for $x$ is $\{x:x\le \frac{-1}{2},x\in R\}$.