Hi,

Apologies this is a simple problem but yet I have forgotten how to solve since school days

.

The problem is :

**(x/6) = (x/2) - (4/3)**

The explanation to the answer is:

| |

(x/6) = (x/2) - (4/3) | / Find a common denominator. |

(2x/12) = (6x/12) - (16/12) | / Multiply both sides by 12 |

2x = 6x - 16 | / Subtract 6x from each side. |

-4x = -16 | / Divide each side by -4. |

x = -16/-4 | |

**x = 4**
| |

Sorry I don't understand the explanation. Where is the 16 from?

Thanks

\(\displaystyle \dfrac{x}{6} = \dfrac{x}{2} - \dfrac{4}{3}.\)

I have no idea why they suggest multiplying by 12. It's easier and just as effective to multiply by 6. In any case, here is a step by step following their suggestion.

\(\displaystyle \dfrac{x}{6} = \dfrac{x}{2} - \dfrac{4}{3} \implies 12 * \dfrac{x}{6} = 12 * \left(\dfrac{x}{2} - \dfrac{4}{3}\right).\) Multiplying both sides of the equation by 12 as suggested.

\(\displaystyle 12 * \dfrac{x}{6} = 12 * \left(\dfrac{x}{2} - \dfrac{4}{3}\right) \implies \dfrac{12x}{6} = \dfrac{12x}{2} - \dfrac{12 * 4}{3}\)

\(\displaystyle \implies 2x = 6x - \dfrac{48}{3}\)

\(\displaystyle \implies 2x = 6x - 16\)

\(\displaystyle \implies 2x + 16 = 6x - 16 + 16\)

\(\displaystyle \implies 2x + 16 = 6x\)

\(\displaystyle \implies 6x = 2x + 16\)

\(\displaystyle \implies - 2x + 6x = - 2x + 2x + 16\)

\(\displaystyle \implies 6x - 2x = 16\)

\(\displaystyle \implies 4x = 16\)

\(\displaystyle \implies \dfrac{4x}{4} = \dfrac{16}{4}\)

\(\displaystyle \implies x = 4.\)