What is \textit{substitution}? \begin{solutionordottedlines}[2cm] The replacement of pronumerals or variables with numerical values in an algebraic expression. \end{solutionordottedlines} \begin{boxdef} \textbf{Pronumeral:} \begin{solutionordottedlines}[2cm] A symbol used to represent a number in algebraic expressions and equations. \end{solutionordottedlines} \end{boxdef} \begin{boxdef} \textbf{Numerical Value:} \begin{solutionordottedlines}[2cm] A specific number represented by a symbol or an expression. \end{solutionordottedlines} \end{boxdef} \begin{examplebox} \subsection{Examples} \begin{doublespace} \begin{questions} \Question[1] Evaluate $ 2x $ when $ x = 3 $ \begin{solutionordottedlines}[1cm] $2 \times 3 = 6$ \end{solutionordottedlines} \Question[1] Evaluate $ 5a + 2b $ when $ a = 2 $ and $ b = -3 $ \begin{solutionordottedlines}[1cm] $5 \times 2 + 2 \times (-3) = 10 - 6 = 4$ \end{solutionordottedlines} \Question[1] Evaluate $ 2p(3q-2) $ when $ p = 1 $ and $ q = -2 $ \begin{solutionordottedlines}[1cm] $2 \times 1 \times (3 \times (-2) - 2) = 2 \times (-6 - 2) = 2 \times (-8) = -16$ \end{solutionordottedlines} \Question[1] Evaluate $ 7m - 4n $ when $ m = -3 $ and $ n = -2 $ \begin{solutionordottedlines}[1cm] $7 \times (-3) - 4 \times (-2) = -21 + 8 = -13$ \end{solutionordottedlines} \Question[1] Evaluate $ a + 2b - 3c $ when $ a = 3, b = -5, c = -2 $ \begin{solutionordottedlines}[1cm] $3 + 2 \times (-5) - 3 \times (-2) = 3 - 10 + 6 = -1$ \end{solutionordottedlines} \end{questions} \end{doublespace} \end{examplebox} \newpage \begin{exercisebox} \subsection{Exercises} \begin{questions} \Question[2] Evaluate \(2x-3y\) when: \begin{parts} \begin{multicols}{2} \part \(x = \frac{2}{5}, y = -\frac{1}{4}\) \begin{solutionordottedlines}[1cm] $2 \times \frac{2}{5} - 3 \times \left(-\frac{1}{4}\right) = \frac{4}{5} + \frac{3}{4} = \frac{16}{20} + \frac{15}{20} = \frac{31}{20} = 1\frac{11}{20}$ \end{solutionordottedlines} \part \(x = \frac{1}{3}, y = \frac{1}{6}\) \begin{solutionordottedlines}[1cm] $2 \times \frac{1}{3} - 3 \times \frac{1}{6} = \frac{2}{3} - \frac{3}{6} = \frac{2}{3} - \frac{1}{2} = \frac{4}{6} - \frac{3}{6} = \frac{1}{6}$ \end{solutionordottedlines} \end{multicols} \end{parts} \Question[2] Evaluate \(p^2 -2q\) when: \begin{parts} \begin{multicols}{2} \part \(p=-7, q = 2\) \begin{solutionordottedlines}[1cm] $(-7)^2 - 2 \times 2 = 49 - 4 = 45$ \end{solutionordottedlines} \part \(p = -\frac{1}{3}, q = \frac{5}{6}\) \begin{solutionordottedlines}[1cm] $\left(-\frac{1}{3}\right)^2 - 2 \times \frac{5}{6} = \frac{1}{9} - \frac{10}{6} = \frac{1}{9} - \frac{15}{9} = -\frac{14}{9} = -1\frac{5}{9}$ \end{solutionordottedlines} \end{multicols} \end{parts} \end{questions} \end{exercisebox}