6.4.2 Linear Equations, PT3 Practice - Mathematics

Question 4:

Solve the following linear equations.

\begin{array}{l} (a) 11 + \frac{2 x}{3} = 9 \\ (b) \frac{x - 5}{3} = \frac{x}{6} \end{array}

Solution:

\begin{array}{l} (a) 11 + \frac{2 x}{3} = 9 \\ \frac{2 x}{3} = 9 - 11 \\ \frac{2 x}{3} = - 2 \\ 2 x = - 6 \\ x = \frac{- 6}{2} \\ x = - 3 \end{array}

\begin{array}{l} (b) \frac{x - 5}{3} = \frac{x}{6} \\ 6 (x - 5) = 3 x \\ 6 x - 30 = 3 x \\ 6 x - 3 x = 30 \\ 3 x = 30 \\ x = 10 \end{array}

Question 5:

Solve the following linear equations.

\begin{array}{l} (a) 4 (2 x - 3) = 24 \\ (b) \frac{y}{2} - \frac{y + 4}{3} = 5 \end{array}

Solution:

\begin{array}{l} (a) 4 (2 x - 3) = 24 \\ 8 x - 12 = 24 \\ 8 x = 24 + 12 \\ 8 x = 36 \\ x = \frac{36}{8} \\ x = 4 \frac{1}{2} \end{array}

\begin{array}{l} (b) \frac{y}{2} - \frac{y + 4}{3} = 5 \\ \frac{y \times 3}{2 \times 3} - \frac{2 (y + 4)}{3 \times 2} = 5 \\ \frac{3 y - 2 (y + 4)}{6} = 5 \\ 3 y - 2 y - 8 = 30 \\ y = 30 + 8 \\ y = 38 \end{array}

Question 6:
Solve each of the following equations:

\begin{array}{l} (a) 5 a - 16 = a \\ (b) 6 + \frac{2}{3} (- 9 p + 12) = p \end{array}

Solution:
(a)

\begin{array}{l} 5 a - 16 = a \\ 5 a - a = 16 \\ 4 a = 16 \\ a = 4 \end{array}

(b)

\begin{array}{l} 6 + \frac{2}{3} (- 9 p + 12) = p \\ 6 - 6 p + 8 = p \\ - 6 p - p = - 8 - 6 \\ - 7 p = - 14 \\ p = 2 \end{array}