QUESTION 8
Easy
Find the rational number \(x\) such that:
\(\frac{5}{6}(x + \frac{3}{5}) = \frac{5}{6}x + \frac{1}{2}\)
SOLUTION
The given equation is
\(\frac{5}{6}(x + \frac{3}{5}) = \frac{5}{6}x + \frac{1}{2}\)
⇒ \(\frac{5}{6}(x) + \frac{5}{6} × \frac{3}{5} = \frac{5}{6}x + \frac{1}{2}\)
⇒ \(\frac{5}{6}x + \frac{5 × 3}{6 × 5} = \frac{5}{6}x + \frac{1}{2}\)
⇒ \(\frac{5}{6}x + \frac{15}{30} = \frac{5}{6}x + \frac{1}{2}\)
⇒ \(\frac{5}{6}x + \frac{1}{2} = \frac{5}{6}x + \frac{1}{2}\)
LHS = RHS
This means that the equation will be true for any value of \(x\).
\(\frac{5}{6}(x + \frac{3}{5}) = \frac{5}{6}x + \frac{1}{2}\)
⇒ \(\frac{5}{6}(x) + \frac{5}{6} × \frac{3}{5} = \frac{5}{6}x + \frac{1}{2}\)
⇒ \(\frac{5}{6}x + \frac{5 × 3}{6 × 5} = \frac{5}{6}x + \frac{1}{2}\)
⇒ \(\frac{5}{6}x + \frac{15}{30} = \frac{5}{6}x + \frac{1}{2}\)
⇒ \(\frac{5}{6}x + \frac{1}{2} = \frac{5}{6}x + \frac{1}{2}\)
LHS = RHS
This means that the equation will be true for any value of \(x\).