Find the value of x in the following expression:
\(\frac{5}{6} \div \frac{6}{7} \times x - \frac{8}{9} \div 1\frac{3}{5} + \frac{3}{4} \times 3\frac{1}{3} = 2\frac{7}{9}\)
Solution
Correct Answer: Option C
Follow BODMAS rule to solve this question, as per the order given below,
Step-1-Parts of an equation enclosed in 'Brackets' must be solved first,
Step-2-Any mathematical 'Of' or 'Exponent' must be solved next,
Step-3-Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,
Step-4-Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.
Given expression:
\(\begin{array}{l} \frac{5}{6} \div \frac{6}{7} \times x - \frac{8}{9} \div 1\frac{3}{5} + \frac{3}{4} \times 3\frac{1}{3} = 2\frac{7}{9}\\ \Rightarrow \frac{5}{6} \div \frac{6}{7} \times x - \frac{8}{9} \div \frac{{5 \times 1 + 3}}{5} + \frac{3}{4} \times \frac{{3 \times 3 + 1}}{3} = \frac{{9 \times 2 + 7}}{9}\\ \Rightarrow \frac{5}{6} \div \frac{6}{7} \times x - \frac{8}{9} \div \frac{8}{5} + \frac{3}{4} \times \frac{{10}}{3} = \frac{{25}}{9}\\ \Rightarrow \left( {\frac{5}{6} \times \frac{7}{6}} \right) \times x - \left( {\frac{8}{9} \times \frac{5}{8}} \right) + \frac{3}{4} \times \frac{{10}}{3} = \frac{{25}}{9}\\ \Rightarrow \frac{{35}}{{36}} \times x - \frac{5}{9} + \frac{5}{2} = \frac{{25}}{9}\\ \Rightarrow \frac{{35}}{{36}} \times x - \left( {\frac{{10 - 45}}{{18}}} \right) = \frac{{25}}{9}\\ \Rightarrow \frac{{35}}{{36}} \times x + \frac{{35}}{{18}} = \frac{{25}}{9}\\ \Rightarrow \frac{{35}}{{36}} \times x = \frac{{25}}{9} - \frac{{35}}{{18}}\\ \Rightarrow \frac{{35}}{{36}} \times x = \frac{{50 - 35}}{{18}}\\ \Rightarrow \frac{{35}}{{36}} \times x = \frac{{15}}{{18}}\\ \Rightarrow x = \frac{{15}}{{18}} \times \frac{{36}}{{35}}\\ \Rightarrow x = \frac{6}{7} \end{array}\)
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