Question

$verify [tex]x = \frac{3}{4} \: \: y = \frac{5}{6} \: \: z = \frac{ - 7}{8}$[/tex]
​

Answer 1

$[tex]x = (y + z) = (x + y) + z \\ \\ x = (y + z) = \frac{3}{4} + ( \frac{5}{6} + \frac{ - 7}{8} ) \\ \\ = \frac{3}{4} + ( \frac{20 + ( - 21)}{24} ) \\ \\ = \frac{3}{4} + ( \frac{ - 1}{24} ) \\ \\ = \frac{3}{4} + \frac{ - 1}{24} \\ \\ = \frac{18 + ( - 1)}{24} \\ \\ = \frac{17}{24} \\ \\ (x + y ) + z = ( \frac{3}{4} + \frac{5}{6} ) + \frac{ - 7}{8} \\ \\ = ( \frac{9 + 10}{12} ) + \frac{ - 7}{8} \\ \\ = \frac{19}{12} + \frac{ - 7}{8} \\ \\ = \frac{38 + ( - 21)}{24} \\ \\ = \frac{38 - 21}{24} \\ \\ = \frac{17}{24} \\ \\ x + (y + z) = (x + y) + z$

verified[/tex]

Answer 2

To verify x + (y +z) = (x+y) + z

where,

$x = \frac{3}{4} \: \: y = \frac{5}{6} \: \: z = \frac{ - 7}{8}$

$x + (y + z) = (x + y) + z \\ = > \frac{3}{4} + ( \frac{5}{6} + \frac{ - 7}{8} ) = ( \frac{3}{4} + \frac{5}{6} ) + \frac{ - 7}{8} \\ = > \frac{3}{4} + ( \frac{(5 \times 4) + ( - 7 \times 3)}{24} ) = ( \frac{(3 \times 3) + (5 \times 2)}{12} + \frac{ - 7}{8} \\ = > \frac{3}{4} + (\frac{20 - 21}{24} ) = ( \frac{9 + 10}{12} ) + \frac{ - 7}{8} \\ = > \frac{3}{4} + \frac{ - 1}{24} = \frac{19}{12} + \frac{ - 7}{8} \\ = > \frac{(3 \times 6) + ( - 1)}{24} = \frac{(19 \times 2) + ( - 7 \times 3)}{24} \\ = > \frac{18 - 1}{24} = \frac{38 - 21}{24} \\ = > \frac{17}{24} = \frac{17}{24} \\ = > LHS \: = RHS \: \\ hence \: verified \\ hope \: it \: helps$