Solve 8y-44/5/5+y/4=-59/40

$$\frac{ \frac{ 8y-44 }{ 5 } }{ 5 } + \frac{ y }{ 4 } = \frac{ -59 }{ 40 }$$

Solve for y

$$y=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 5,4,40.

$$8\times \frac{8y-44}{5}+10y=-59$$

Express 8\times \frac{8y-44}{5} as a single fraction.

$$\frac{8\left(8y-44\right)}{5}+10y=-59$$

Use the distributive property to multiply 8 by 8y-44.

$$\frac{64y-352}{5}+10y=-59$$

Divide each term of 64y-352 by 5 to get \frac{64}{5}y-\frac{352}{5}.

$$\frac{64}{5}y-\frac{352}{5}+10y=-59$$

Combine \frac{64}{5}y and 10y to get \frac{114}{5}y.

$$\frac{114}{5}y-\frac{352}{5}=-59$$

Add \frac{352}{5} to both sides.

$$\frac{114}{5}y=-59+\frac{352}{5}$$

Convert -59 to fraction -\frac{295}{5}.

$$\frac{114}{5}y=-\frac{295}{5}+\frac{352}{5}$$

Since -\frac{295}{5} and \frac{352}{5} have the same denominator, add them by adding their numerators.

$$\frac{114}{5}y=\frac{-295+352}{5}$$

Add -295 and 352 to get 57.

$$\frac{114}{5}y=\frac{57}{5}$$

Multiply both sides by \frac{5}{114}, the reciprocal of \frac{114}{5}.

$$y=\frac{57}{5}\times \frac{5}{114}$$

Multiply \frac{57}{5} times \frac{5}{114} by multiplying numerator times numerator and denominator times denominator.

$$y=\frac{57\times 5}{5\times 114}$$

Cancel out 5 in both numerator and denominator.

$$y=\frac{57}{114}$$

Reduce the fraction \frac{57}{114} to lowest terms by extracting and canceling out 57.

$$y=\frac{1}{2}$$