# 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$

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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,

$\Rightarrow (\frac{3p}{3})=\frac{60}{3}$

$\Rightarrow p=20$

Updated on 10-Oct-2022 13:33:38