Solve the following equations:
$(a).\ 4=5(p-2)$
$(b).\ -4=5(p-2)$
$(c).\ 16=4+3(t+2)$
$(d).\ 4+5(p-1)=34$
$(e).\ 0=16+4(m-6)$

To do:

We have to solve the given equations.

Solution:

(a) $4=5(p-2)$

$\Rightarrow 4=5p-10$

$\Rightarrow 5p=4+10$

$\Rightarrow 5p=14$

$\Rightarrow p=\frac{14}{5}$

(b) $-4=5(p-2)$

$\Rightarrow -4=5p-10$

$\Rightarrow -4+10=5p$

$\Rightarrow 6=5p$

$\Rightarrow p=\frac{6}{5}$

(c) $16=4+3(t+2)$

$\Rightarrow 16=4+3t+6$

$\Rightarrow 16-10=3t$

$\Rightarrow 6=3t$

$\Rightarrow t=\frac{6}{3}$

$\Rightarrow t=2$

(d) $4+5(p-1)=34$

$\Rightarrow 4+5p-5=34$

$\Rightarrow 5p-1=34$

$\Rightarrow 5p=34+1$

$\Rightarrow 5p=35$

$\Rightarrow p=\frac{35}{5}$

$\Rightarrow p=7$

(e) $0=16+4(m-6)$

$\Rightarrow 0=16+4m-24$

$\Rightarrow 0=4m-8$

$\Rightarrow 8=4m$

$\Rightarrow m=\frac{8}{4}$

$\Rightarrow m=2$