Question

2/3*(-5/7)+2/3+7/3*(-2/7)​

Answer 1

y=55/21 or 2 13/21

PREMISES

-2/3×(-5/7)+7/3+2/3×(-2/7)=y

CALCULATIONS

y=[(-2/3)(-5/7)]+7/3+[(2/3)(-2/7)]

y=(-2×-5)/(3×7)+7/3+(2×-2)/(3×7)

y=10/21+7/3+-4/21 (Convert all fractions to the LCD=21 to simplify the math)

y=(10/21+49/21)+-4/21

y=(10+49)/21+-4/21

y=59/21+-4/21

y=(59–4)/21

y=55/21

y=

55/21 or 2 13/21 as a mixed fraction

PROOF

If y=55/21, then the equations

y=59/21–4/21

55/21=59/21–4/21

55/21=(59–4)/21 and

55/21=55/21 establish that y=55/21 is a solution to the equation (-2/3)(-5/7)+7/3+(2/3)(-2/7)=y