Solve 3y+1/5=3y-7/3

$$\frac { 3 y + 1 } { 5 } = \frac { 3 y - 7 } { 3 }$$

Solve for y

$$y = \frac{19}{3} = 6\frac{1}{3} \approx 6.333333333$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3.

$$3\left(3y+1\right)=5\left(3y-7\right)$$

Use the distributive property to multiply 3 by 3y+1.

$$9y+3=5\left(3y-7\right)$$

Use the distributive property to multiply 5 by 3y-7.

$$9y+3=15y-35$$

Subtract 15y from both sides.

$$9y+3-15y=-35$$

Combine 9y and -15y to get -6y.

$$-6y+3=-35$$

Subtract 3 from both sides.

$$-6y=-35-3$$

Subtract 3 from -35 to get -38.

$$-6y=-38$$

Divide both sides by -6.

$$y=\frac{-38}{-6}$$

Reduce the fraction \frac{-38}{-6} to lowest terms by extracting and canceling out -2.

$$y=\frac{19}{3}$$