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Give the steps you will use to separate the variable and then solve the equation:
$(a).\ 3n-2=46$
$(b).\ 5m+7=17$
$(c).\ \frac{20p}{3}=40$
$(d).\ \frac{3p}{10}=6$
To do:
We have to give the steps you will use to separate the variable and then solve the equation.
Solution:
(a) $3n-2=46$
Adding 2 to both sides of the equation, we get
$\Rightarrow 3n-2+2=46+2$
$\Rightarrow 3n=48$
Dividing both the sides by 3 we get,
$\Rightarrow \frac{3n}{3}=\frac{48}{3}$
$\Rightarrow n=16$
(b) $5m+7=17$
Subtracting 7 from both sides of the equation, we get
$\Rightarrow 5m+7-7=17-7$
$\Rightarrow 5m=10$
Dividing both the sides by 5 we get,
$\Rightarrow \frac{5m}{5}=\frac{10}{5}$
$\Rightarrow m=2$
(c) $\frac{20p}{3}=40$
Multiplying both the sides by 3 we get,
$\Rightarrow (\frac{20p}{3})\times 3=40\times 3$
$\Rightarrow 20p=120$
Dividing both the sides by 20 we get,
$\Rightarrow \frac{20p}{20}=\frac{120}{20}$
$\Rightarrow p=6$
(d) $\frac{3p}{10}=6$
Multiplying both the sides by 10 we get,
$\Rightarrow (\frac{3p}{10})\times 10=6\times 10$
$\Rightarrow 3p=60$
Dividing both the sides by 3 we get,
$\Rightarrow (\frac{3p}{3})=\frac{60}{3}$
$\Rightarrow p=20$