Solve the following equation and check your answer:

5(3 - x) + 1 = 3(x + 4)

We have:

5(3 - x) + 1 = 3(x + 4)

⇒ 15 - 5x + 1 = 3x + 12 $\quad$[Removing brackets]

⇒ 16 - 5x = 3x + 12

⇒ 16 - 12 = 3x + 5x $\quad$[Transposing -5x to RHS and +12 to LHS]

⇒ 4 = 8x

⇒ x = $\dfrac{4}{8}$

∴ x = $\dfrac{1}{2}$

Check:

$\text{LHS} = 5(3 - x) + 1 \\[1em] \phantom{\text{LHS}} = 5\left(3 - \dfrac{1}{2}\right) + 1 \\[1em] \phantom{\text{LHS}} = 5\left(\dfrac{5}{2}\right) + 1 \\[1em] \phantom{\text{LHS}} = \dfrac{25}{2} + 1 \\[1em] \phantom{\text{LHS}} = \dfrac{27}{2} \\[2em] \text{RHS} = 3(x + 4) \\[1em] \phantom{\text{RHS}} = 3\left(\dfrac{1}{2} + 4\right) \\[1em] \phantom{\text{RHS}} = 3\left(\dfrac{9}{2}\right) \\[1em] \phantom{\text{RHS}} = \dfrac{27}{2}$

Hence, LHS = RHS.