Question

If $x=p+1$, find the value of $p$ from the equation $\frac{1}{2}(5x-30)-\frac{1}{3}(1+7p)=\frac{1}{4}$

Answer 1

Simplifying $\frac{1}{2}\left(5x-30\right)-\frac{1}{3}\left(1+7p\right)=\frac{1}{4}$

$\frac{1}{2}\left(5x-30\right)-\frac{1}{3}\left(1+7p\right)=\frac{1}{4}$

$\frac{5}{2}x-15-\frac{1}{3}-\frac{7}{3}p=\frac{1}{4}$

$\frac{5}{2}\left(p+1\right)-\frac{7}{3}p-\frac{46}{3}=\frac{1}{4}$

$\frac{5}{2}p+\frac{5}{2}-\frac{7}{3}p=\frac{1}{4}+\frac{46}{3}$

$\frac{15p-14p}{6}=\frac{177}{12}-\frac{5}{2}$

$\frac{p}{6}=d\frac{147}{12}$

$p=\frac{147}{12}\times 6$

$p=\frac{147}{2}$