Solve 3x-(10x-[4x-[7x+y-5]+(-x+2y)+y+x])

$$3 x - ( 10 x - [ 4 x - [ 7 x + y - 5 ] + ( - x + 2 y ) + y + x ] )$$

Evaluate

$$5+2y-10x$$

Solution Steps

To find the opposite of 7x+y-5, find the opposite of each term.

$$3x-\left(10x-\left(4x-7x-y-\left(-5\right)-x+2y+y+x\right)\right)$$

The opposite of -5 is 5.

$$3x-\left(10x-\left(4x-7x-y+5-x+2y+y+x\right)\right)$$

Combine 4x and -7x to get -3x.

$$3x-\left(10x-\left(-3x-y+5-x+2y+y+x\right)\right)$$

Combine -y and 2y to get y.

$$3x-\left(10x-\left(-3x+y+5-x+y+x\right)\right)$$

Combine y and y to get 2y.

$$3x-\left(10x-\left(-3x+2y+5-x+x\right)\right)$$

Combine -3x and x to get -2x.

$$3x-\left(10x-\left(-2x+2y+5-x\right)\right)$$

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

$$3x-\left(10x-\left(-2x\right)-2y-5-\left(-x\right)\right)$$

The opposite of -2x is 2x.

$$3x-\left(10x+2x-2y-5-\left(-x\right)\right)$$

Combine 10x and 2x to get 12x.

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

To find the opposite of 12x-2y-5-\left(-x\right), find the opposite of each term.

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

Combine 3x and -12x to get -9x.

$$-9x-\left(-2y\right)-\left(-5\right)-\left(-\left(-x\right)\right)$$

The opposite of -2y is 2y.

$$-9x+2y-\left(-5\right)-\left(-\left(-x\right)\right)$$

The opposite of -5 is 5.

$$-9x+2y+5-\left(-\left(-x\right)\right)$$

Multiply -1 and -1 to get 1.

$$-9x+2y+5-x$$

Combine -9x and -x to get -10x.

$$-10x+2y+5$$

Expand

$$5+2y-10x$$

Solution Steps

To find the opposite of 7x+y-5, find the opposite of each term.

$$3x-\left(10x-\left(4x-7x-y-\left(-5\right)-x+2y+y+x\right)\right)$$

The opposite of -5 is 5.

$$3x-\left(10x-\left(4x-7x-y+5-x+2y+y+x\right)\right)$$

Combine 4x and -7x to get -3x.

$$3x-\left(10x-\left(-3x-y+5-x+2y+y+x\right)\right)$$

Combine -y and 2y to get y.

$$3x-\left(10x-\left(-3x+y+5-x+y+x\right)\right)$$

Combine y and y to get 2y.

$$3x-\left(10x-\left(-3x+2y+5-x+x\right)\right)$$

Combine -3x and x to get -2x.

$$3x-\left(10x-\left(-2x+2y+5-x\right)\right)$$

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

$$3x-\left(10x-\left(-2x\right)-2y-5-\left(-x\right)\right)$$

The opposite of -2x is 2x.

$$3x-\left(10x+2x-2y-5-\left(-x\right)\right)$$

Combine 10x and 2x to get 12x.

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

To find the opposite of 12x-2y-5-\left(-x\right), find the opposite of each term.

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

Combine 3x and -12x to get -9x.

$$-9x-\left(-2y\right)-\left(-5\right)-\left(-\left(-x\right)\right)$$

The opposite of -2y is 2y.

$$-9x+2y-\left(-5\right)-\left(-\left(-x\right)\right)$$

The opposite of -5 is 5.

$$-9x+2y+5-\left(-\left(-x\right)\right)$$

Multiply -1 and -1 to get 1.

$$-9x+2y+5-x$$

Combine -9x and -x to get -10x.

$$-10x+2y+5$$