Question

Solve each of the following system of equations in R.

23. $\left|\frac{3x-4}{2}\right|\le \frac{5}{12}$

Answer 1

$$\begin{gathered} \mathrm{We}have\left|\frac{3x-4}{2}\right|\le \frac{5}{12} \\ \Rightarrow \left|\frac{3}{2}\left(x-\frac{4}{3}\right)\right|\le \frac{5}{12} \\ \Rightarrow \frac{3}{2}\left|x-\frac{4}{3}\right|\le \frac{5}{12} \\ \Rightarrow \left|x-\frac{4}{3}\right|\le \frac{5}{12}\times \frac{2}{3} \\ \Rightarrow \left|x-\frac{4}{3}\right|\le \frac{5}{18} \\ \mathrm{We}\mathrm{know}: \\ \left|x-a\right|\le r\Rightarrow a-r\le x\le a+r \\ \Rightarrow \frac{4}{3}-\frac{5}{18}\le x\le \frac{4}{3}+\frac{5}{18} \\ \Rightarrow \frac{24-5}{18}\le x\le \frac{24+5}{18} \\ \Rightarrow \frac{19}{18}\le x\le \frac{29}{18} \\ \Rightarrow x\in \left[\frac{19}{18},\frac{29}{18}\right] \end{gathered}$$