Solve 3-2(y-5)/8=6-(10-y)/5

$$\frac { 3 - 2 ( y - 5 ) } { 8 } = \frac { 6 - ( 10 - y ) } { 5 }$$

Solve for y

$$y = \frac{97}{18} = 5\frac{7}{18} \approx 5.388888889$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 8,5.

$$5\left(3-2\left(y-5\right)\right)=8\left(6-\left(10-y\right)\right)$$

Use the distributive property to multiply -2 by y-5.

$$5\left(3-2y+10\right)=8\left(6-\left(10-y\right)\right)$$

Add 3 and 10 to get 13.

$$5\left(13-2y\right)=8\left(6-\left(10-y\right)\right)$$

Use the distributive property to multiply 5 by 13-2y.

$$65-10y=8\left(6-\left(10-y\right)\right)$$

To find the opposite of 10-y, find the opposite of each term.

$$65-10y=8\left(6-10-\left(-y\right)\right)$$

The opposite of -y is y.

$$65-10y=8\left(6-10+y\right)$$

Subtract 10 from 6 to get -4.

$$65-10y=8\left(-4+y\right)$$

Use the distributive property to multiply 8 by -4+y.

$$65-10y=-32+8y$$

Subtract 8y from both sides.

$$65-10y-8y=-32$$

Combine -10y and -8y to get -18y.

$$65-18y=-32$$

Subtract 65 from both sides.

$$-18y=-32-65$$

Subtract 65 from -32 to get -97.

$$-18y=-97$$

Divide both sides by -18.

$$y=\frac{-97}{-18}$$

Fraction \frac{-97}{-18} can be simplified to \frac{97}{18} by removing the negative sign from both the numerator and the denominator.

$$y=\frac{97}{18}$$