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

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

Solve for x

$$x=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Use the distributive property to multiply -3 by x-1.

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

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

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

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

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

The opposite of -2x is 2x.

$$4x-2+2x-3=3x-6$$

Combine 4x and 2x to get 6x.

$$6x-2-3=3x-6$$

Subtract 3 from -2 to get -5.

$$6x-5=3x-6$$

Subtract 3x from both sides.

$$6x-5-3x=-6$$

Combine 6x and -3x to get 3x.

$$3x-5=-6$$

Add 5 to both sides.

$$3x=-6+5$$

Add -6 and 5 to get -1.

$$3x=-1$$

Divide both sides by 3.

$$x=\frac{-1}{3}$$

Fraction \frac{-1}{3} can be rewritten as -\frac{1}{3} by extracting the negative sign.

$$x=-\frac{1}{3}$$