Solve -[3x+8-[-15+6x-(-3x+2)-(5x+4)]-29]=

$$- [ 3 x + 8 - [ - 15 + 6 x - ( - 3 x + 2 ) - ( 5 x + 4 ) ] - 29 ] =$$

Evaluate

$$x$$

Solution Steps

To find the opposite of -3x+2, find the opposite of each term.

$$-\left(3x+8-\left(-15+6x-\left(-3x\right)-2-\left(5x+4\right)\right)-29\right)$$

The opposite of -3x is 3x.

$$-\left(3x+8-\left(-15+6x+3x-2-\left(5x+4\right)\right)-29\right)$$

Combine 6x and 3x to get 9x.

$$-\left(3x+8-\left(-15+9x-2-\left(5x+4\right)\right)-29\right)$$

Subtract 2 from -15 to get -17.

$$-\left(3x+8-\left(-17+9x-\left(5x+4\right)\right)-29\right)$$

To find the opposite of 5x+4, find the opposite of each term.

$$-\left(3x+8-\left(-17+9x-5x-4\right)-29\right)$$

Combine 9x and -5x to get 4x.

$$-\left(3x+8-\left(-17+4x-4\right)-29\right)$$

Subtract 4 from -17 to get -21.

$$-\left(3x+8-\left(-21+4x\right)-29\right)$$

To find the opposite of -21+4x, find the opposite of each term.

$$-\left(3x+8-\left(-21\right)-4x-29\right)$$

The opposite of -21 is 21.

$$-\left(3x+8+21-4x-29\right)$$

Add 8 and 21 to get 29.

$$-\left(3x+29-4x-29\right)$$

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

$$-\left(-x+29-29\right)$$

Subtract 29 from 29 to get 0.

$$-\left(-x\right)$$

The opposite of -x is x.

$$x$$

Differentiate w.r.t. x

$$1$$

Steps Using Definition of a Derivative

To find the opposite of -3x+2, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8-\left(-15+6x-\left(-3x\right)-2-\left(5x+4\right)\right)-29\right))$$

The opposite of -3x is 3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8-\left(-15+6x+3x-2-\left(5x+4\right)\right)-29\right))$$

Combine 6x and 3x to get 9x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8-\left(-15+9x-2-\left(5x+4\right)\right)-29\right))$$

Subtract 2 from -15 to get -17.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8-\left(-17+9x-\left(5x+4\right)\right)-29\right))$$

To find the opposite of 5x+4, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8-\left(-17+9x-5x-4\right)-29\right))$$

Combine 9x and -5x to get 4x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8-\left(-17+4x-4\right)-29\right))$$

Subtract 4 from -17 to get -21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8-\left(-21+4x\right)-29\right))$$

To find the opposite of -21+4x, find the opposite of each term.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8-\left(-21\right)-4x-29\right))$$

The opposite of -21 is 21.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+8+21-4x-29\right))$$

Add 8 and 21 to get 29.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(3x+29-4x-29\right))$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(-x+29-29\right))$$

Subtract 29 from 29 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\left(-x\right))$$

The opposite of -x is x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The derivative of ax^{n} is nax^{n-1}.

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$