Solve 7/6=-9/7y-4/3

$$\frac { 7 } { 6 } = - \frac { 9 } { 7 } y - \frac { 4 } { 3 }$$

Solve for y

$$y = -\frac{35}{18} = -1\frac{17}{18} \approx -1.944444444$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$-\frac{9}{7}y-\frac{4}{3}=\frac{7}{6}$$

Add \frac{4}{3} to both sides.

$$-\frac{9}{7}y=\frac{7}{6}+\frac{4}{3}$$

Least common multiple of 6 and 3 is 6. Convert \frac{7}{6} and \frac{4}{3} to fractions with denominator 6.

$$-\frac{9}{7}y=\frac{7}{6}+\frac{8}{6}$$

Since \frac{7}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$-\frac{9}{7}y=\frac{7+8}{6}$$

Add 7 and 8 to get 15.

$$-\frac{9}{7}y=\frac{15}{6}$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

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

Multiply both sides by -\frac{7}{9}, the reciprocal of -\frac{9}{7}.

$$y=\frac{5}{2}\left(-\frac{7}{9}\right)$$

Multiply \frac{5}{2} times -\frac{7}{9} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{5\left(-7\right)}{2\times 9}$$

Do the multiplications in the fraction \frac{5\left(-7\right)}{2\times 9}.

$$y=\frac{-35}{18}$$

Fraction \frac{-35}{18} can be rewritten as -\frac{35}{18} by extracting the negative sign.

$$y=-\frac{35}{18}$$