Solve -8(5y/8-9/4)+5y=18

$$- 8 ( \frac { 5 y } { 8 } - \frac { 9 } { 4 } ) + 5 y = 18$$

Solve for y (complex solution)

$$y\in \mathrm{C}$$

Short Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 8,4.

$$-64\left(\frac{5y}{8}-\frac{9}{4}\right)+40y=144$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 4 is 8. Multiply \frac{9}{4} times \frac{2}{2}.

$$-64\left(\frac{5y}{8}-\frac{9\times 2}{8}\right)+40y=144$$

Since \frac{5y}{8} and \frac{9\times 2}{8} have the same denominator, subtract them by subtracting their numerators.

$$-64\times \frac{5y-9\times 2}{8}+40y=144$$

Do the multiplications in 5y-9\times 2.

$$-64\times \frac{5y-18}{8}+40y=144$$

Cancel out 8, the greatest common factor in 64 and 8.

$$-8\left(5y-18\right)+40y=144$$

Use the distributive property to multiply -8 by 5y-18.

$$-40y+144+40y=144$$

Combine -40y and 40y to get 0.

$$144=144$$

Compare 144 and 144.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{C}$$

Solve for y

$$y\in \mathrm{R}$$

Short Solution Steps

Multiply both sides of the equation by 8, the least common multiple of 8,4.

$$-64\left(\frac{5y}{8}-\frac{9}{4}\right)+40y=144$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8 and 4 is 8. Multiply \frac{9}{4} times \frac{2}{2}.

$$-64\left(\frac{5y}{8}-\frac{9\times 2}{8}\right)+40y=144$$

Since \frac{5y}{8} and \frac{9\times 2}{8} have the same denominator, subtract them by subtracting their numerators.

$$-64\times \frac{5y-9\times 2}{8}+40y=144$$

Do the multiplications in 5y-9\times 2.

$$-64\times \frac{5y-18}{8}+40y=144$$

Cancel out 8, the greatest common factor in 64 and 8.

$$-8\left(5y-18\right)+40y=144$$

Use the distributive property to multiply -8 by 5y-18.

$$-40y+144+40y=144$$

Combine -40y and 40y to get 0.

$$144=144$$

Compare 144 and 144.

$$\text{true}$$

This is true for any y.

$$y\in \mathrm{R}$$