**Question 6:**Solve each of the following equations:

$\begin{array}{l}\text{(a)}5a-16=a\\ \text{(b)}6+\frac{2}{3}\left(-9p+12\right)=p\end{array}$

*Solution*:(a)

$\begin{array}{l}5a-16=a\\ 5a-a=16\\ 4a=16\\ a=4\end{array}$

(b)

$\begin{array}{l}6+\frac{2}{3}\left(-9p+12\right)=p\\ 6-6p+8=p\\ -6p-p=-8-6\\ -7p=-14\\ p=2\end{array}$

**:**

**Question 7:**Solve each of the following equations:

$\begin{array}{l}\text{(a)}a-2=\frac{a}{5}\\ \text{(b)}\frac{b-3}{4}=\frac{2+b}{5}\end{array}$

*Solution:*(a)

$\begin{array}{l}a-2=\frac{a}{5}\\ 5a-2=a\\ 4a=2\\ a=2\end{array}$

(b)

$\begin{array}{l}\frac{b-3}{4}=\frac{2+b}{5}\\ 5b-15=8+4b\\ 5b-4b=8+15\\ b=23\end{array}$

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**Question 8:**Solve each of the following equations:

$\begin{array}{l}\text{(a)}x=-24-x\\ \text{(b)}y+\frac{5}{4}\left(4-2y\right)=-4\end{array}$

**Solution:**(a)

$\begin{array}{l}x=-24-x\\ 2x=-24\\ x=-12\end{array}$

(b)

$\begin{array}{l}y+\frac{5}{4}\left(4-2y\right)=-4\\ 4y+20-10y=-16\text{}\left(\times 4\right)\\ -6y=-16-20\\ -6y=-36\\ y=6\end{array}$

**Question 9:**Solve each of the following equations:

$\begin{array}{l}\text{(a)}5p=8p-9\\ \text{(b)}3q=\frac{20-13q}{4}\end{array}$

**Solution:**(a)

$\begin{array}{l}5p=8p-9\\ 5p-8p=-9\\ -3p=-9\\ p=3\end{array}$

(b)

$\begin{array}{l}3q=\frac{20-13q}{4}\\ 12q=20-13q\\ 12q+13q=20\\ 25q=20\\ q=\frac{4}{5}\end{array}$