Question

Give first the step you will use to separate the variable and then solve the equation: 
(a) 3l = 42 
(b) \(\frac{b}{2}\)= 6 
(c) \(\frac{p}{7}\) = 4 
(d) 4x = 25 
(e) 8y = 36 
(f) \(\frac{z}{3}\)=\(\frac{5}{4}\)
(g) \(\frac{a}{5}\)=\(\frac{7}{15}\)
(h) 20t = – 10

Answer 1

(a) \(3l=42\)
\(\Rightarrow\)\(\frac{3l}{3}=\frac{42}{3}\)
\(\Rightarrow l=14\) [Dividing both sides by 3]

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(b) \(\frac{b}{2}=6\)
\(\Rightarrow \frac{b}{2}\times2=6\times 2\)
\(\Rightarrow b=12\)

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(c) \(\frac{p}{7}=4\)
\(\Rightarrow  \frac{p}{7}\times 7=4\times7\)
\(\Rightarrow p=28\)

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(d) \(4x=25\)
\(\Rightarrow \frac{4x}{4}=\frac{25}{4}\)
\(\Rightarrow x=\frac{25}{4}\)

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(e) 8y = 36
\(\Rightarrow\frac{8y}{8}=\frac{36}{8}\)
(f) \(\frac{z}{3}=\frac{5}{4}\)
\(\Rightarrow\)\(\frac{a}{5}\times5=\frac{7}{15}\times 5\)
\(\Rightarrow z=\frac{7}{3}\)

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(g) \(\frac{a}{5}\)=\(\frac{7}{15}\)
\(\Rightarrow \frac{a}{5}\times 5=\frac{7}{15}\times 5\)

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\((h)\,20t=-10\)
\(\Rightarrow \frac{20t}{20}=\frac{-10}{20}\)
\(\Rightarrow t=\frac{-1}{2}\)