Question

the value of x in 2 x/6 + 4 5/12 = 6 7/12 is

Answer 1

Correct Question :-

The value of x in $\tt 2 \dfrac{x}{6} + 4\dfrac{5}{12} = 6 \dfrac{7}{12}$ is

Solution :-

$\tt 2 \dfrac{x}{6} + 4\dfrac{5}{12} = 6 \dfrac{7}{12}$

First convert every term i.e mixed fraction to improper faction

$\tt \dfrac{6(2) + x}{6} + \dfrac{12(4) + 5}{12} = \dfrac{12(6) + 7}{12}$

$\tt \dfrac{12+ x}{6} + \dfrac{48 + 5}{12} = \dfrac{72 + 7}{12}$

$\tt \dfrac{12+ x}{6} + \dfrac{53}{12} = \dfrac{79}{12}$

$\tt \dfrac{12+ x}{6} = \dfrac{79}{12} - \dfrac{53}{12}$

$\tt \dfrac{12+ x}{6} = \dfrac{79 - 53}{12}$

$\tt \dfrac{12+ x}{6} = \dfrac{26}{12}$

$\tt 12+ x= \dfrac{26}{12} \times 6$

$\tt 12+ x= \dfrac{26}{2}$

$\tt x= \dfrac{26}{2} - 12$

$\tt x= \dfrac{26}{2} - \dfrac{12(2)}{1(2)}$

$\tt x= \dfrac{26}{2} - \dfrac{24}{2}$

$\tt x= \dfrac{26 - 24}{2}$

$\tt x= \dfrac{2}{2}$

$\tt x= \dfrac{2 \div 2}{2 \div 2}$

$\tt x= \dfrac{1}{1}$

$\tt x = 1$

$\Huge{\boxed{ \sf x = 1}}$

Verification :-

$\tt 2 \dfrac{x}{6} + 4\dfrac{5}{12} = 6 \dfrac{7}{12}$

$\tt 2 \dfrac{1}{6} + 4\dfrac{5}{12} = 6 \dfrac{7}{12}$

$\tt \dfrac{6(2) +1}{6} + \dfrac{12(4) + 5}{12} = \dfrac{12(6) + 7}{12}$

$\tt \dfrac{13}{6} + \dfrac{53}{12} = \dfrac{79}{12}$

$\tt \dfrac{13(2)}{6(2)} + \dfrac{53}{12} = \dfrac{79}{12}$

$\tt \dfrac{26}{12} + \dfrac{53}{12} = \dfrac{79}{12}$

$\tt \dfrac{26 + 53}{12}= \dfrac{79}{12}$

$\tt \dfrac{79}{12}= \dfrac{79}{12}$

Answer 2

$2 \: \dfrac{x}{6} \: + \: 4 \: \dfrac{5}{12} \: = \: 6 \: \dfrac{7}{12}$

_________ [GIVEN EQUATION]

• We have to find the value of x.

______________________________

$2 \: \dfrac{x}{6} \: + \: 4 \: \dfrac{5}{12} \: = \: 6 \: \dfrac{7}{12}$

=> $\dfrac{6(2) \: + \: x}{6} \: + \dfrac{12(4) \: + \: 5}{12} \: = \: \dfrac{12(6) \: + \: 7}{12}$

=> $\dfrac{12 \: + \: x}{6} \: + \dfrac{48 \: + \: 5}{12} \: = \: \dfrac{72 \: + \: 7}{12}$

=> $\dfrac{12 \: + \: x}{6} \: + \dfrac{53}{12} \: = \: \dfrac{79}{12}$

=> $\dfrac{12 \: + \: x}{6} \: = \: \dfrac{79}{12} \: - \: \dfrac{53}{12}$

=> $\dfrac{12 \: + \: x}{6} \: = \: \dfrac{79\:-\:53}{12}$

=> $\dfrac{12 \: + \: x}{6} \: = \: \dfrac{26}{12}$

=> => $\dfrac{12 \: + \: x}{6} \: = \: \dfrac{13}{6}$

=> 12 + x = $\dfrac{13}{6}$ × 6

=> 12 + x = 13

=> x = 13 - 12

______________________________

x = 1

___________ [ANSWER]