Solve 4x-[x-(x-1)+4x]=6-2[5+3(x+2)]+4

$$4 x - [ x - ( x - 1 ) + 4 x ] = 6 - 2 [ 5 + 3 ( x + 2 ) ] + 4$$

Solve for x

$$x = -\frac{11}{6} = -1\frac{5}{6} \approx -1.833333333$$

Steps for Solving Linear Equation

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

$$4x-\left(x-x-\left(-1\right)+4x\right)=6-2\left(5+3\left(x+2\right)\right)+4$$

The opposite of -1 is 1.

$$4x-\left(x-x+1+4x\right)=6-2\left(5+3\left(x+2\right)\right)+4$$

Combine x and -x to get 0.

$$4x-\left(1+4x\right)=6-2\left(5+3\left(x+2\right)\right)+4$$

To find the opposite of 1+4x, find the opposite of each term.

$$4x-1-4x=6-2\left(5+3\left(x+2\right)\right)+4$$

Combine 4x and -4x to get 0.

$$-1=6-2\left(5+3\left(x+2\right)\right)+4$$

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

$$-1=6-2\left(5+3x+6\right)+4$$

Add 5 and 6 to get 11.

$$-1=6-2\left(11+3x\right)+4$$

Use the distributive property to multiply -2 by 11+3x.

$$-1=6-22-6x+4$$

Subtract 22 from 6 to get -16.

$$-1=-16-6x+4$$

Add -16 and 4 to get -12.

$$-1=-12-6x$$

Swap sides so that all variable terms are on the left hand side.

$$-12-6x=-1$$

Add 12 to both sides.

$$-6x=-1+12$$

Add -1 and 12 to get 11.

$$-6x=11$$

Divide both sides by -6.

$$x=\frac{11}{-6}$$

Fraction \frac{11}{-6} can be rewritten as -\frac{11}{6} by extracting the negative sign.

$$x=-\frac{11}{6}$$