Solve y=8+3-34+10y/7

$$y = 8+3 \frac{ -34+10y }{ 7 }$$

Solve for y

$$y=2$$

Steps for Solving Linear Equation

Express 3\times \frac{-34+10y}{7} as a single fraction.

$$y=8+\frac{3\left(-34+10y\right)}{7}$$

Use the distributive property to multiply 3 by -34+10y.

$$y=8+\frac{-102+30y}{7}$$

Divide each term of -102+30y by 7 to get -\frac{102}{7}+\frac{30}{7}y.

$$y=8-\frac{102}{7}+\frac{30}{7}y$$

Convert 8 to fraction \frac{56}{7}.

$$y=\frac{56}{7}-\frac{102}{7}+\frac{30}{7}y$$

Since \frac{56}{7} and \frac{102}{7} have the same denominator, subtract them by subtracting their numerators.

$$y=\frac{56-102}{7}+\frac{30}{7}y$$

Subtract 102 from 56 to get -46.

$$y=-\frac{46}{7}+\frac{30}{7}y$$

Subtract \frac{30}{7}y from both sides.

$$y-\frac{30}{7}y=-\frac{46}{7}$$

Combine y and -\frac{30}{7}y to get -\frac{23}{7}y.

$$-\frac{23}{7}y=-\frac{46}{7}$$

Multiply both sides by -\frac{7}{23}, the reciprocal of -\frac{23}{7}.

$$y=-\frac{46}{7}\left(-\frac{7}{23}\right)$$

Multiply -\frac{46}{7} times -\frac{7}{23} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{-46\left(-7\right)}{7\times 23}$$

Do the multiplications in the fraction \frac{-46\left(-7\right)}{7\times 23}.

$$y=\frac{322}{161}$$

Divide 322 by 161 to get 2.

$$y=2$$