Question

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

Answer 1

(a) 3n – 2 = 46
Step 1 : 
3n – 2+2= 46+2
3n=48
Step 2 : 
\(\frac{3n}{3}\)=\(\frac{48}{3}\)
\(\Rightarrow n=16\)

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(b) 5m+7=17
Step 1 : 
5m+7-7=17-7
\(\Rightarrow 5m=10\)[Subtracting 7 both sides] 
Step 2 : 
\(\frac{5m}{5}=\frac{10}{5}\)[Dividing both sides by 5] 
\(m=2\)

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(c) \(\frac{20p}{3}\) =40
Step 1 : 
 \(\frac{20p}{3}\times 3\) =40\(\times 3\) [Multiplying both sides by 3] 
Step 2 : 
\(\frac{3p}{3}=\frac{60}{3}\)
\(\Rightarrow p=20\) [Dividing both sides by 20]

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(d) \(\frac{3p}{10}\)=6
Step 1 : 
 \(\frac{3p}{10}\times 10\)=\(6\times 10\)
\(\Rightarrow 3p=60\) [Multiplying both sides by 10] 
Step 2 : 
\(\frac{3p}{3}=\frac{60}{3}\)
\(p=20\) [Dividing both sides by 3]