Tìm số ngyên x biết:
a) \(\frac{{ - 5}}{7} + 1 + \frac{{30}}{{ - 7}} \le x \le \frac{{ - 1}}{6} + \frac{1}{3} + \frac{5}{6}\)
b) \(\frac{{ - 8}}{{13}} + \frac{7}{{17}} + \frac{{21}}{{13}} \le x \le \frac{{ - 9}}{{14}} + 3 + \frac{5}{{ - 14}}\)
Tính hai phép cộng phân số, chặn giá trị của x.
a)
Ta có:
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\(\begin{array}{l}\frac{{ - 5}}{7} + 1 + \frac{{30}}{{ - 7}} = \left( {\frac{{ - 5}}{7} + \frac{{30}}{{ - 7}}} \right) + 1 = \left( {\frac{{ - 5}}{7} + \frac{{ - 30}}{7}} \right) + 1 = \frac{{ - 35}}{7} + 1 = - 5 + 1 = - 4\\\frac{{ - 1}}{6} + \frac{1}{3} + \frac{5}{6} = \left( {\frac{{ - 1}}{6} + \frac{5}{6}} \right) + \frac{1}{3} = \frac{4}{6} + \frac{1}{3} = \frac{2}{3} + \frac{1}{3} = 1\end{array}\)
Do đó:
\(\frac{{ - 5}}{7} + 1 + \frac{{30}}{{ - 7}} \le x \le \frac{{ - 1}}{6} + \frac{1}{3} + \frac{5}{6} \Leftrightarrow - 4 \le x \le 1 \Leftrightarrow x \in \left\{ { - 4; - 3; - 2; - 1;0;1} \right\}\)vì x là số nguyên.
Vậy \(x \in \left\{ { - 4; - 3; - 2; - 1;0;1} \right\}\)
b) Ta có:
\(\begin{array}{l}\frac{{ - 8}}{{13}} + \frac{7}{{17}} + \frac{{21}}{{13}} = \left( {\frac{{ - 8}}{{13}} + \frac{{21}}{{13}}} \right) + \frac{7}{{17}} = \frac{{13}}{{13}} + \frac{7}{{17}} = 1 + \frac{7}{{17}} = \frac{{24}}{{17}}\\\frac{{ - 9}}{{14}} + 3 + \frac{5}{{ - 14}} = \left( {\frac{{ - 9}}{{14}} + \frac{5}{{ - 14}}} \right) + 3 = \left( {\frac{{ - 9}}{{14}} + \frac{{ - 5}}{{14}}} \right) + 3 = \frac{{ - 14}}{{14}} + 3 = - 1 + 3 = 2\end{array}\)
Do đó:
\(\frac{{ - 8}}{{13}} + \frac{7}{{17}} + \frac{{21}}{{13}} \le x \le \frac{{ - 9}}{{14}} + 3 + \frac{5}{{ - 14}} \Leftrightarrow \frac{{24}}{{17}} \le x \le 2 \Rightarrow x = 2\) vì x là số nguyên.
Vậy x = 2.