Question

Mark (✓) against the correct answer:
$\frac{x+5}{2}+\frac{x-5}{3}=\frac{25}{6}\mathrm{gives}$
(a) x = 3
(b) x = 4
(c) x = 5
(d) x = 2

Answer 1

(b) $x=4$


$$\begin{gathered} \frac{x+5}{2}+\frac{x-5}{3}=\frac{25}{6} \\ \Rightarrow \frac{3\left(x+5\right)+2\left(x-5\right)}{6}=\frac{25}{6}\left(\mathrm{because}\mathrm{L}.\mathrm{C}.\mathrm{M}.\mathrm{of}2\&3\mathrm{is}6\right) \\ \Rightarrow \frac{3x+15+2x-10}{6}=\frac{25}{6} \\ \Rightarrow \frac{5x+5}{6}=\frac{25}{6} \\ \Rightarrow 5x+5=25\left(\mathrm{cancelling}6\mathrm{from}\mathrm{the}\mathrm{denominator}\mathrm{on}\mathrm{both}\mathrm{the}\mathrm{sides}\right) \\ \Rightarrow 5x=25-5 \\ \Rightarrow 5x=20 \\ \Rightarrow x=\frac{20}{5} \\ \Rightarrow x=4 \end{gathered}$$