💣 Q :85 Prep 1 Question Bank T1

a) Find the value of \( X \) in: \(\frac{-5}{12} - \left( -\frac{7}{6} \right) = \frac{1}{6} + X\)

\[ \begin{align*} \frac{-5}{12} - \left( -\frac{7}{6} \right) &= \frac{1}{6} + X \\ \frac{-5}{12} + \frac{7}{6} &= \frac{1}{6} + X \\ \frac{-5}{12} + \frac{14}{12} &= \frac{1}{6} + X \\ \frac{9}{12} &= \frac{1}{6} + X \\ \frac{3}{4} - \frac{1}{6} &= X \\ \frac{9}{12} - \frac{2}{12} &= X \\ X &= \frac{7}{12} \end{align*} \]

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b) Find the value of \( X \) in: \(\frac{2}{7} - \left( -\frac{11}{21} \right) = \frac{11}{21} - X\)

\[ \begin{align*} \frac{2}{7} - \left( -\frac{11}{21} \right) &= \frac{11}{21} - X \\ \frac{2}{7} + \frac{11}{21} &= \frac{11}{21} - X \\ \frac{6}{21} + \frac{11}{21} &= \frac{11}{21} - X \\ \frac{17}{21} &= \frac{11}{21} - X \\ X &= \frac{11}{21} - \frac{17}{21} \\ X &= \frac{-6}{21} \\ X &= \frac{-2}{7} \end{align*} \]

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c) Find the value of \( X \) in: \(0.6 - \left( -\frac{1}{3} \right) = 30 \, \% + X\)

\[ \begin{align*} 0.6 - \left( -\frac{1}{3} \right) &= 30\% + X \\ 0.6 + \frac{1}{3} &= 0.3 + X \\ \frac{3}{5} + \frac{1}{3} &= 0.3 + X \\ \frac{9}{15} + \frac{5}{15} &= 0.3 + X \\ \frac{14}{15} &= 0.3 + X \\ \frac{14}{15} - \frac{3}{10} &= X \\ \frac{28}{30} - \frac{9}{30} &= X \\ X &= \frac{19}{30} \end{align*} \]

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