Solve 6(-9/2x+9y-3/2)+8(8x+7y-5/4)

$$6 ( - \frac { 9 } { 2 } x + 9 y - \frac { 3 } { 2 } ) + 8 ( 8 x + 7 y - \frac { 5 } { 4 } )$$

Evaluate

$$37x+110y-19$$

Solution Steps

Use the distributive property to multiply 6 by -\frac{9}{2}x+9y-\frac{3}{2}.

$$6\left(-\frac{9}{2}\right)x+54y+6\left(-\frac{3}{2}\right)+8\left(8x+7y-\frac{5}{4}\right)$$

Express 6\left(-\frac{9}{2}\right) as a single fraction.

$$\frac{6\left(-9\right)}{2}x+54y+6\left(-\frac{3}{2}\right)+8\left(8x+7y-\frac{5}{4}\right)$$

Multiply 6 and -9 to get -54.

$$\frac{-54}{2}x+54y+6\left(-\frac{3}{2}\right)+8\left(8x+7y-\frac{5}{4}\right)$$

Divide -54 by 2 to get -27.

$$-27x+54y+6\left(-\frac{3}{2}\right)+8\left(8x+7y-\frac{5}{4}\right)$$

Express 6\left(-\frac{3}{2}\right) as a single fraction.

$$-27x+54y+\frac{6\left(-3\right)}{2}+8\left(8x+7y-\frac{5}{4}\right)$$

Multiply 6 and -3 to get -18.

$$-27x+54y+\frac{-18}{2}+8\left(8x+7y-\frac{5}{4}\right)$$

Divide -18 by 2 to get -9.

$$-27x+54y-9+8\left(8x+7y-\frac{5}{4}\right)$$

Use the distributive property to multiply 8 by 8x+7y-\frac{5}{4}.

$$-27x+54y-9+64x+56y+8\left(-\frac{5}{4}\right)$$

Express 8\left(-\frac{5}{4}\right) as a single fraction.

$$-27x+54y-9+64x+56y+\frac{8\left(-5\right)}{4}$$

Multiply 8 and -5 to get -40.

$$-27x+54y-9+64x+56y+\frac{-40}{4}$$

Divide -40 by 4 to get -10.

$$-27x+54y-9+64x+56y-10$$

Combine -27x and 64x to get 37x.

$$37x+54y-9+56y-10$$

Combine 54y and 56y to get 110y.

$$37x+110y-9-10$$

Subtract 10 from -9 to get -19.

$$37x+110y-19$$

Expand

$$37x+110y-19$$

Solution Steps

Use the distributive property to multiply 6 by -\frac{9}{2}x+9y-\frac{3}{2}.

$$6\left(-\frac{9}{2}\right)x+54y+6\left(-\frac{3}{2}\right)+8\left(8x+7y-\frac{5}{4}\right)$$

Express 6\left(-\frac{9}{2}\right) as a single fraction.

$$\frac{6\left(-9\right)}{2}x+54y+6\left(-\frac{3}{2}\right)+8\left(8x+7y-\frac{5}{4}\right)$$

Multiply 6 and -9 to get -54.

$$\frac{-54}{2}x+54y+6\left(-\frac{3}{2}\right)+8\left(8x+7y-\frac{5}{4}\right)$$

Divide -54 by 2 to get -27.

$$-27x+54y+6\left(-\frac{3}{2}\right)+8\left(8x+7y-\frac{5}{4}\right)$$

Express 6\left(-\frac{3}{2}\right) as a single fraction.

$$-27x+54y+\frac{6\left(-3\right)}{2}+8\left(8x+7y-\frac{5}{4}\right)$$

Multiply 6 and -3 to get -18.

$$-27x+54y+\frac{-18}{2}+8\left(8x+7y-\frac{5}{4}\right)$$

Divide -18 by 2 to get -9.

$$-27x+54y-9+8\left(8x+7y-\frac{5}{4}\right)$$

Use the distributive property to multiply 8 by 8x+7y-\frac{5}{4}.

$$-27x+54y-9+64x+56y+8\left(-\frac{5}{4}\right)$$

Express 8\left(-\frac{5}{4}\right) as a single fraction.

$$-27x+54y-9+64x+56y+\frac{8\left(-5\right)}{4}$$

Multiply 8 and -5 to get -40.

$$-27x+54y-9+64x+56y+\frac{-40}{4}$$

Divide -40 by 4 to get -10.

$$-27x+54y-9+64x+56y-10$$

Combine -27x and 64x to get 37x.

$$37x+54y-9+56y-10$$

Combine 54y and 56y to get 110y.

$$37x+110y-9-10$$

Subtract 10 from -9 to get -19.

$$37x+110y-19$$