Chapter 3
The World of Numbers
CBSE Class 9
Mathematics Solutions
Educart Mathematics class Class 9 NCERT Exemplar cover
Question:

Find the rational number xx such that

56(x+35)=56x+12. [Page No. 49]\frac{5}{6} \left(x + \frac{3}{5}\right) = \frac{5}{6} x + \frac{1}{2}. \text{ [Page No. 49]}

Answer: Verified

Expand LHS using distributive law:

(56)x+(56)(35)=(56)x+12\left(\frac{5}{6}\right)x + \left(\frac{5}{6}\right)\left(\frac{3}{5}\right) = \left(\frac{5}{6}\right)x + \frac{1}{2}

(56)x+1530=(56)x+12\left(\frac{5}{6}\right)x + \frac{15}{30} = \left(\frac{5}{6}\right)x + \frac{1}{2}

(56)x+12=(56)x+12\left(\frac{5}{6}\right)x + \frac{1}{2} = \left(\frac{5}{6}\right)x + \frac{1}{2}

This is true for every rational number xx. So, any rational number xx satisfies the equation.

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