Question

Solve the following inequation and graph the solution set on the number line: $x+\frac{2}{15}\le -\frac{8}{15},x\in R$.

Answer 1

Step 1: Solve the given inequality

$$\begin{gathered} \Rightarrow x+\frac{2}{15}\le -\frac{8}{15} \\ \Rightarrow x\le -\frac{8}{15}-\frac{2}{15} \\ \Rightarrow x\le -\frac{10}{15} \\ \Rightarrow x\le -\frac{2}{3} \end{gathered}$$

Hence, the required solution set is $\{x:x\le -\frac{2}{3},x\in R\}$

Step 2: Represent the solution set on a number line:

Thus, the solution set of the given inequality is $\mathbf{\{}\mathbf{x}\mathbf{:}\mathbf{x}\mathbf{\le }\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}}\mathbf{,}\mathbf{x}\mathbf{\in }\mathbf{R}\mathbf{\}}$