Tìm \(x \in \mathbb{Z}\) để các biểu thức sau có giá trị nguyên.

a) \(A = \frac{5}{{2x - 3}}\);

c) \[\frac{{x - 214}}{{86}} + \frac{{x - 132}}{{84}} + \frac{{x - 54}}{{82}} = 6\]

\[x\left( {\frac{1}{{86}} + \frac{1}{{84}} + \frac{1}{{82}}} \right) = 6 + \frac{{214}}{{86}} + \frac{{132}}{{84}} + \frac{{54}}{{82}}\]

\[x\left( {\frac{1}{{86}} + \frac{1}{{84}} + \frac{1}{{82}}} \right) = \left( {1 + \frac{{214}}{{86}}} \right) + \left( {2 + \frac{{132}}{{84}}} \right) + \left( {3 + \frac{{54}}{{82}}} \right)\]

\[x\left( {\frac{1}{{86}} + \frac{1}{{84}} + \frac{1}{{82}}} \right) = \frac{{300}}{{86}} + \frac{{300}}{{84}} + \frac{{300}}{{82}}\]

\[x\left( {\frac{1}{{86}} + \frac{1}{{84}} + \frac{1}{{82}}} \right) = 300\left( {\frac{1}{{86}} + \frac{1}{{84}} + \frac{1}{{82}}} \right)\]

\[x = 300\]

Vậy \[x = 300\].

a) Ta có: \(\widehat {MNz} = \widehat {xMy} = 60^\circ \) (gt)

Mà hai góc ở vị trí đồng vị nên \(My\parallel Nz.\)

b) Ta có: \(My\parallel Pt\) (gt) mà \(My\parallel Nz\) (cmt) nên \(Nz\parallel Pt.\)

c) Ta có: \(\widehat {xNz} + \widehat {zNP} = \widehat {xNP} = 85^\circ \) nên \(\widehat {zNP} = \widehat {xNP} - xNz = 85^\circ - 60^\circ = 25^\circ \).

Có \(Nz\parallel Pt\) nên \(\widehat {zNP} = \widehat {NPt} = 25^\circ \).

Vậy \(\widehat {NPt} = 25^\circ \).