Solve 9/14y-5/7=-11/2

$$\frac { 9 } { 14 } y - \frac { 5 } { 7 } = - \frac { 11 } { 2 }$$

Solve for y

$$y = -\frac{67}{9} = -7\frac{4}{9} \approx -7.444444444$$

Steps for Solving Linear Equation

Add \frac{5}{7} to both sides.

$$\frac{9}{14}y=-\frac{11}{2}+\frac{5}{7}$$

Least common multiple of 2 and 7 is 14. Convert -\frac{11}{2} and \frac{5}{7} to fractions with denominator 14.

$$\frac{9}{14}y=-\frac{77}{14}+\frac{10}{14}$$

Since -\frac{77}{14} and \frac{10}{14} have the same denominator, add them by adding their numerators.

$$\frac{9}{14}y=\frac{-77+10}{14}$$

Add -77 and 10 to get -67.

$$\frac{9}{14}y=-\frac{67}{14}$$

Multiply both sides by \frac{14}{9}, the reciprocal of \frac{9}{14}.

$$y=-\frac{67}{14}\times \frac{14}{9}$$

Multiply -\frac{67}{14} times \frac{14}{9} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-67\times 14}{14\times 9}$$

Cancel out 14 in both numerator and denominator.

$$y=\frac{-67}{9}$$

Fraction \frac{-67}{9} can be rewritten as -\frac{67}{9} by extracting the negative sign.

$$y=-\frac{67}{9}$$