Solve [-3(x+6)+2(4x+8)-x]-(3x-4)=2[x-(7x-1)]

$$[ - 3 ( x + 6 ) + 2 ( 4 x + 8 ) - x ] - ( 3 x - 4 ) = 2 [ x - ( 7 x - 1 ) ]$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x+6.

$$-3x-18+2\left(4x+8\right)-x-\left(3x-4\right)=2\left(x-\left(7x-1\right)\right)$$

Use the distributive property to multiply 2 by 4x+8.

$$-3x-18+8x+16-x-\left(3x-4\right)=2\left(x-\left(7x-1\right)\right)$$

Combine -3x and 8x to get 5x.

$$5x-18+16-x-\left(3x-4\right)=2\left(x-\left(7x-1\right)\right)$$

Add -18 and 16 to get -2.

$$5x-2-x-\left(3x-4\right)=2\left(x-\left(7x-1\right)\right)$$

Combine 5x and -x to get 4x.

$$4x-2-\left(3x-4\right)=2\left(x-\left(7x-1\right)\right)$$

To find the opposite of 3x-4, find the opposite of each term.

$$4x-2-3x-\left(-4\right)=2\left(x-\left(7x-1\right)\right)$$

The opposite of -4 is 4.

$$4x-2-3x+4=2\left(x-\left(7x-1\right)\right)$$

Combine 4x and -3x to get x.

$$x-2+4=2\left(x-\left(7x-1\right)\right)$$

Add -2 and 4 to get 2.

$$x+2=2\left(x-\left(7x-1\right)\right)$$

To find the opposite of 7x-1, find the opposite of each term.

$$x+2=2\left(x-7x-\left(-1\right)\right)$$

The opposite of -1 is 1.

$$x+2=2\left(x-7x+1\right)$$

Combine x and -7x to get -6x.

$$x+2=2\left(-6x+1\right)$$

Use the distributive property to multiply 2 by -6x+1.

$$x+2=-12x+2$$

Add 12x to both sides.

$$x+2+12x=2$$

Combine x and 12x to get 13x.

$$13x+2=2$$

Subtract 2 from both sides.

$$13x=2-2$$

Subtract 2 from 2 to get 0.

$$13x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 13 is not equal to 0, x must be equal to 0.

$$x=0$$