Persiapan Ulangan 4

Jawab: B

Bisa dimisalkan bilangan-bilangan tersebut:

\(a = -2, b = -3, c = -4\)

(1)   \(a - b > 0\)

\begin{equation*}
\begin{split}
a - b & > 0 \\\\
-2 - (-3) & > 0 \\\\
-2 + 3 & > 0 \\\\
1 & > 0 \quad {\color {red} \text{Benar}}
\end{split}
\end{equation*}

(2)   \(c - b > 0\)

\begin{equation*}
\begin{split}
c - b & > 0 \\\\
-4 - (-3) & > 0 \\\\
-4 + 3 & > 0 \\\\
-1 & > 0 \quad {\color {red} \text{Salah}}
\end{split}
\end{equation*}

(3)   \(\dfrac 1a < \dfrac 1b < \dfrac 1c\)

\begin{equation*}
\begin{split}
\frac 1a & < \frac 1b < \frac 1c \\\\
\frac {1}{-2} & < \frac {1}{-3} < \frac {1}{-4} \\\\
-\frac {1}{2} & < -\frac {1}{3} < -\frac {1}{4} \\\\
-\frac {6}{12} & < -\frac {4}{12} < -\frac {3}{12} \quad {\color {red} \text{Benar}}
\end{split}
\end{equation*}

(4)   \(\dfrac 1b - \dfrac 1c > 0\)

\begin{equation*}
\begin{split}
\frac 1b - \frac 1c & > 0 \\\\
\frac {1}{-3} - \frac {1}{-4} & > 0 \\\\
-\frac {1}{3} + \frac {1}{4} & > 0 \\\\
-\frac {4}{12} + \frac {3}{12} & > 0 \\\\
-\frac {1}{12} & > 0 \quad {\color {red} \text{Salah}}
\end{split}
\end{equation*}