Solve 1.5(2x-y-2)-2[3(x-2y+4)-5(2x-3y+2)]}

$$1.5 ( 2 x - y - 2 ) - 2 [ 3 ( x - 2 y + 4 ) - 5 ( 2 x - 3 y + 2 ) ] \}$$

Evaluate

$$-\frac{39y}{2}+17x-7$$

Solution Steps

Use the distributive property to multiply 1.5 by 2x-y-2.

$$3x-1.5y-3-2\left(3\left(x-2y+4\right)-5\left(2x-3y+2\right)\right)$$

Use the distributive property to multiply 3 by x-2y+4.

$$3x-1.5y-3-2\left(3x-6y+12-5\left(2x-3y+2\right)\right)$$

Use the distributive property to multiply -5 by 2x-3y+2.

$$3x-1.5y-3-2\left(3x-6y+12-10x+15y-10\right)$$

Combine 3x and -10x to get -7x.

$$3x-1.5y-3-2\left(-7x-6y+12+15y-10\right)$$

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

$$3x-1.5y-3-2\left(-7x+9y+12-10\right)$$

Subtract 10 from 12 to get 2.

$$3x-1.5y-3-2\left(-7x+9y+2\right)$$

Use the distributive property to multiply -2 by -7x+9y+2.

$$3x-1.5y-3+14x-18y-4$$

Combine 3x and 14x to get 17x.

$$17x-1.5y-3-18y-4$$

Combine -1.5y and -18y to get -19.5y.

$$17x-19.5y-3-4$$

Subtract 4 from -3 to get -7.

$$17x-19.5y-7$$

Expand

$$-\frac{39y}{2}+17x-7$$

Solution Steps

Use the distributive property to multiply 1.5 by 2x-y-2.

$$3x-1.5y-3-2\left(3\left(x-2y+4\right)-5\left(2x-3y+2\right)\right)$$

Use the distributive property to multiply 3 by x-2y+4.

$$3x-1.5y-3-2\left(3x-6y+12-5\left(2x-3y+2\right)\right)$$

Use the distributive property to multiply -5 by 2x-3y+2.

$$3x-1.5y-3-2\left(3x-6y+12-10x+15y-10\right)$$

Combine 3x and -10x to get -7x.

$$3x-1.5y-3-2\left(-7x-6y+12+15y-10\right)$$

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

$$3x-1.5y-3-2\left(-7x+9y+12-10\right)$$

Subtract 10 from 12 to get 2.

$$3x-1.5y-3-2\left(-7x+9y+2\right)$$

Use the distributive property to multiply -2 by -7x+9y+2.

$$3x-1.5y-3+14x-18y-4$$

Combine 3x and 14x to get 17x.

$$17x-1.5y-3-18y-4$$

Combine -1.5y and -18y to get -19.5y.

$$17x-19.5y-3-4$$

Subtract 4 from -3 to get -7.

$$17x-19.5y-7$$