Tìm x ∈ Z , biết rằng biểu thức: k) − 5/3 ⋅ 1/2 + 8/3 + 29 − 3 ⋅ 1/2 ≤ x ≤ − 1/2 + 2 + 5/2 .
Giải thích
k\(\frac{{ - 5}}{3} \cdot \frac{1}{2} + \frac{8}{3} + \frac{{29}}{{ - 3}} \cdot \frac{1}{2} \le x \le \frac{{ - 1}}{2} + 2 + \frac{5}{2}.\)
\[\frac{1}{2} \cdot \left( {\frac{{ - 5}}{3} + \frac{{ - 29}}{3}} \right) + \frac{8}{3} \le x \le \frac{{ - 1}}{2} + \frac{4}{2} + \frac{5}{2}\]
\[\frac{1}{2} \cdot \frac{{ - 34}}{3} + \frac{8}{3} \le x \le \frac{8}{2}\]
\[\frac{{ - 17}}{3} + \frac{8}{3} \le x \le 4\]
\[ - 3 \le x \le 4\]
\[ - 3 \le x \le 4\]
Vì \[x \in \mathbb{Z}\] nên \[x \in \left\{ { - 3;\,\, - 2;\,\, - 1;\,\,0;\,\,1;\,\,2;\,\,3;\,\,4} \right\}\].
Vậy \[x \in \left\{ { - 3;\,\, - 2;\,\, - 1;\,\,0;\,\,1;\,\,2;\,\,3;\,\,4} \right\}\].