Topic Content:
- Linear Equations Containing Fractions
To solve simple equations containing fractions, first eliminate the fractions by multiplying each term with the LCM of the denominators and then solve as usual.
Example 6.3.1:
Solve the following equation
a. \( \frac{15}{x} \scriptsize = 3 \)
b. \( \frac{x}{7} \scriptsize = 4 \)
c. \( \frac{3x \: + \: 5}{5} \scriptsize = 4 \)
d. \( \normalsize \frac{2}{3} \scriptsize x \: – \: \normalsize \frac{8}{5} \scriptsize = 5 \)
e. \( \normalsize \frac{3}{2x} \scriptsize \: + \: \normalsize \frac{1}{6x} \scriptsize = \normalsize \frac{2}{3} \)
f. \( \normalsize \frac{2x \: – \: 5}{4} \scriptsize \: – \: \normalsize \frac{6x}{2} \scriptsize = 0 \)
Solution
a. \( \frac{15}{x} \scriptsize = 3 \)
We have only one denominator, multiply through by the denominator (x)
\( \frac{15}{x} \scriptsize \: \times \: x = 3 \: \times \: x \) \( \frac{15}{\not{x}} \scriptsize \: \times \: \not{\!x} = 3 \: \times \: x \)
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