Give the steps you will use to separate the variable and then solve the equation:
(a) 3n − 2 = 46
(b) 5m + 7 = 17
(c) $\frac{20 p}{3} = 40$
(d) $\frac{3 p}{10} = 6$

Solution

(a) 3n − 2 = 46

Adding 2 to both sides of the given equation, we obtain

3n − 2 + 2 = 46 + 2

3n = 48

Dividing both sides of the given equation by 3, we obtain

$\frac{3 n}{3} = \frac{48}{3}$

n = 16

(b) 5m + 7 = 17

Subtracting 7 from both sides of the given equation, we obtain

5m + 7 − 7 = 17 − 7

5m = 10

Dividing both sides of the given equation by 5, we obtain

$\frac{5 m}{5} = \frac{10}{5} m = 2$

Multiplying both sides of the given equation by 3, we obtain

$\frac{20 p \times 3}{3} = 40 \times 3 20 p = 120$

Dividing both sides of the given equation by 20, we obtain

$\frac{20 p}{20} = \frac{120}{20} p = 6$

(d) $\frac{3 p}{10} = 6$

Multiplying both sides of the given equation by 10, we obtain

$\frac{3 p \times 10}{10} = 6 \times 10 3 p = 60$

Dividing both sides of the given equation by 3, we obtain

$\frac{3 p}{3} = \frac{60}{3}$

p = 20

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