Question

Simplify and solve the following linear equation.
$15(y-4)-2(y-9)+5(y+6)=0$
[3 marks]

Answer 1

$15(y-4)-2(y-9)+5(y+6)=0$
$\Rightarrow 15y-60-2y+18+5y+30=0$
[1 mark]

$\Rightarrow 18y-12=0$
$\Rightarrow 18y=12$
$\Rightarrow y=\frac{12}{18}$
$\Rightarrow y=\frac{2}{3}$
[1 mark]

To check:
$15(y-4)-2(y-9)+5(y+6)=0$
$\Rightarrow 15(\frac{2}{3}-4)-2(\frac{2}{3}-9)+5(\frac{2}{3}+6)=0$
$\Rightarrow 15\left(\frac{2-12}{3}\right)-2\left(\frac{2-27}{3}\right)+5\left(\frac{2+18}{3}\right)=0$
$\Rightarrow 15\times \frac{-10}{3}-2\times \frac{-25}{3}+5\times \frac{20}{3}=0$
$\Rightarrow -50+\frac{50}{3}+\frac{100}{3}=0$
$\Rightarrow -50+\frac{50+100}{3}=0$
$\Rightarrow -50+\frac{150}{3}=0$
$\Rightarrow -50+50=0$
$\Rightarrow 0=0$
$\Rightarrow L.H.S.=R.H.S$
Therefore, it is correct.
[1 mark]