Giải bài 31 trang 38

Đề bài

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) $\frac{-8}{13}+\frac{7}{17}+\frac{21}{13}\le x\le \frac{-9}{14}+3+\frac{5}{-14}$

Lời giải chi tiết

a)

Ta có:

 $\begin{array}{c}\frac{-5}{7}+1+\frac{30}{-7}=\left(\frac{-5}{7}+\frac{30}{-7}\right)+1=\left(\frac{-5}{7}+\frac{-30}{7}\right)+1=\frac{-35}{7}+1=-5+1=-4\\ \frac{-1}{6}+\frac{1}{3}+\frac{5}{6}=\left(\frac{-1}{6}+\frac{5}{6}\right)+\frac{1}{3}=\frac{4}{6}+\frac{1}{3}=\frac{2}{3}+\frac{1}{3}=1\end{array}$

Do đó:

$\frac{-5}{7}+1+\frac{30}{-7}\le x\le \frac{-1}{6}+\frac{1}{3}+\frac{5}{6}\iff -4\le x\le 1\iff x\in \left\{-4;-3;-2;-1;0;1\right\}$vì x là số nguyên.

Vậy $x\in \left\{-4;-3;-2;-1;0;1\right\}$

b) Ta có:

$\begin{array}{c}\frac{-8}{13}+\frac{7}{17}+\frac{21}{13}=\left(\frac{-8}{13}+\frac{21}{13}\right)+\frac{7}{17}=\frac{13}{13}+\frac{7}{17}=1+\frac{7}{17}=\frac{24}{17}\\ \frac{-9}{14}+3+\frac{5}{-14}=\left(\frac{-9}{14}+\frac{5}{-14}\right)+3=\left(\frac{-9}{14}+\frac{-5}{14}\right)+3=\frac{-14}{14}+3=-1+3=2\end{array}$

Do đó:

$\frac{-8}{13}+\frac{7}{17}+\frac{21}{13}\le x\le \frac{-9}{14}+3+\frac{5}{-14}\iff \frac{24}{17}\le x\le 2\Rightarrow x=2$ vì x là số nguyên.

Vậy x = 2.