Appendix A - Appendix A Exercises - Page 1157: 5

$$x \geqslant \frac{7}{2}\,\,\,\,\,\,\,\,{\text{ }}\,{\text{ or }}\,\,\,\,\,\,\,\,\,\,x \leqslant \frac{1}{2}$$

$$\eqalign{ & \left| {2x - 4} \right| \geqslant 3 \cr & {\text{Using the property }}\,\,\left| x \right| \geqslant a\,\,\,\,\, \Leftrightarrow \,\,\,\,x \geqslant a{\text{ or }}x \leqslant - a \cr & {\text{We can write }}\left| {2x - 4} \right| \geqslant 3 \cr & \left| {2x - 4} \right| \geqslant 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,2x - 4 \geqslant 3{\text{ }}\,{\text{ or }}\,2x - 4 \leqslant - 3 \cr & {\text{simplifying}} \cr & \left| {2x - 4} \right| \geqslant 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,2x \geqslant 3 + 4{\text{ }}\,{\text{ or }}\,\,\,\,\,\,\,\,\,2x \leqslant - 3 + 4 \cr & \left| {2x - 4} \right| \geqslant 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,2x \geqslant 7\,\,\,\,\,\,\,\,{\text{ }}\,{\text{ or }}\,\,\,\,\,\,\,\,\,2x \leqslant 1 \cr & \left| {2x - 4} \right| \geqslant 3\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\,x \geqslant \frac{7}{2}\,\,\,\,\,\,\,\,{\text{ }}\,{\text{ or }}\,\,\,\,\,\,\,\,\,\,x \leqslant \frac{1}{2} \cr} $$