Solve 3x-(2y-5x)-[(3x-8y)-(4y-7x)]

$$3 x - ( 2 y - 5 x ) - [ ( 3 x - 8 y ) - ( 4 y - 7 x ) ]$$

Evaluate

$$10y-2x$$

Solution Steps

To find the opposite of 2y-5x, find the opposite of each term.

$$3x-2y-\left(-5x\right)-\left(3x-8y-\left(4y-7x\right)\right)$$

The opposite of -5x is 5x.

$$3x-2y+5x-\left(3x-8y-\left(4y-7x\right)\right)$$

Combine 3x and 5x to get 8x.

$$8x-2y-\left(3x-8y-\left(4y-7x\right)\right)$$

To find the opposite of 4y-7x, find the opposite of each term.

$$8x-2y-\left(3x-8y-4y-\left(-7x\right)\right)$$

The opposite of -7x is 7x.

$$8x-2y-\left(3x-8y-4y+7x\right)$$

Combine -8y and -4y to get -12y.

$$8x-2y-\left(3x-12y+7x\right)$$

Combine 3x and 7x to get 10x.

$$8x-2y-\left(10x-12y\right)$$

To find the opposite of 10x-12y, find the opposite of each term.

$$8x-2y-10x-\left(-12y\right)$$

The opposite of -12y is 12y.

$$8x-2y-10x+12y$$

Combine 8x and -10x to get -2x.

$$-2x-2y+12y$$

Combine -2y and 12y to get 10y.

$$-2x+10y$$

Expand

$$10y-2x$$

Solution Steps

To find the opposite of 2y-5x, find the opposite of each term.

$$3x-2y-\left(-5x\right)-\left(3x-8y-\left(4y-7x\right)\right)$$

The opposite of -5x is 5x.

$$3x-2y+5x-\left(3x-8y-\left(4y-7x\right)\right)$$

Combine 3x and 5x to get 8x.

$$8x-2y-\left(3x-8y-\left(4y-7x\right)\right)$$

To find the opposite of 4y-7x, find the opposite of each term.

$$8x-2y-\left(3x-8y-4y-\left(-7x\right)\right)$$

The opposite of -7x is 7x.

$$8x-2y-\left(3x-8y-4y+7x\right)$$

Combine -8y and -4y to get -12y.

$$8x-2y-\left(3x-12y+7x\right)$$

Combine 3x and 7x to get 10x.

$$8x-2y-\left(10x-12y\right)$$

To find the opposite of 10x-12y, find the opposite of each term.

$$8x-2y-10x-\left(-12y\right)$$

The opposite of -12y is 12y.

$$8x-2y-10x+12y$$

Combine 8x and -10x to get -2x.

$$-2x-2y+12y$$

Combine -2y and 12y to get 10y.

$$-2x+10y$$