Đáp án:
d) \(\left[ \begin{array}{l}
x = 3\\
x = 1\\
x = 0\\
x = - 2\\
x = - 3\\
x = - 5
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a)\dfrac{2}{3} - \dfrac{4}{3}x = \dfrac{1}{2}\\
\to \dfrac{4}{3}x = \dfrac{1}{6}\\
\to x = \dfrac{1}{6}\\
b)175 \vdots x\\
\to x \in U\left( {175} \right)\\
Mà:x < 6;x \in N\\
\to \left[ \begin{array}{l}
x = 1\\
x = 5
\end{array} \right.\\
240 \vdots x\\
\to x \in U\left( {240} \right)\\
Mà:x < 6;x \in N\\
\to \left[ \begin{array}{l}
x = 1\\
x = 2\\
x = 3\\
x = 4\\
x = 5
\end{array} \right.\\
c)DK:x \ne - 7\\
\dfrac{{x + 2}}{{x + 7}} = \dfrac{1}{2}\\
\to 2x + 4 = x + 7\\
\to x = 3\\
d)P = \dfrac{{x + 5}}{{x + 1}} = \dfrac{{x + 1 + 4}}{{x + 1}} = 1 + \dfrac{4}{{x + 1}}\\
P \in Z \Leftrightarrow \dfrac{4}{{x + 1}} \in Z\\
\to x + 1 \in U\left( 4 \right)\\
\to \left[ \begin{array}{l}
x + 1 = 4\\
x + 1 = 2\\
x + 1 = 1\\
x + 1 = - 1\\
x + 1 = - 2\\
x + 1 = - 4
\end{array} \right. \to \left[ \begin{array}{l}
x = 3\\
x = 1\\
x = 0\\
x = - 2\\
x = - 3\\
x = - 5
\end{array} \right.
\end{array}\)
