Solve 12x-3[x-1/2(x-1)]=4(x-1)

$$12 x - 3 [ x - \frac { 1 } { 2 } ( x - 1 ) ] = 4 ( x - 1 )$$

Solve for x

$$x=-\frac{5}{13}\approx -0.384615385$$

Steps for Solving Linear Equation

Use the distributive property to multiply -\frac{1}{2} by x-1.

$$12x-3\left(x-\frac{1}{2}x-\frac{1}{2}\left(-1\right)\right)=4\left(x-1\right)$$

Multiply -\frac{1}{2} and -1 to get \frac{1}{2}.

$$12x-3\left(x-\frac{1}{2}x+\frac{1}{2}\right)=4\left(x-1\right)$$

Combine x and -\frac{1}{2}x to get \frac{1}{2}x.

$$12x-3\left(\frac{1}{2}x+\frac{1}{2}\right)=4\left(x-1\right)$$

Use the distributive property to multiply -3 by \frac{1}{2}x+\frac{1}{2}.

$$12x-3\times \frac{1}{2}x-3\times \frac{1}{2}=4\left(x-1\right)$$

Multiply -3 and \frac{1}{2} to get \frac{-3}{2}.

$$12x+\frac{-3}{2}x-3\times \frac{1}{2}=4\left(x-1\right)$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$12x-\frac{3}{2}x-3\times \frac{1}{2}=4\left(x-1\right)$$

Multiply -3 and \frac{1}{2} to get \frac{-3}{2}.

$$12x-\frac{3}{2}x+\frac{-3}{2}=4\left(x-1\right)$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$12x-\frac{3}{2}x-\frac{3}{2}=4\left(x-1\right)$$

Combine 12x and -\frac{3}{2}x to get \frac{21}{2}x.

$$\frac{21}{2}x-\frac{3}{2}=4\left(x-1\right)$$

Use the distributive property to multiply 4 by x-1.

$$\frac{21}{2}x-\frac{3}{2}=4x-4$$

Subtract 4x from both sides.

$$\frac{21}{2}x-\frac{3}{2}-4x=-4$$

Combine \frac{21}{2}x and -4x to get \frac{13}{2}x.

$$\frac{13}{2}x-\frac{3}{2}=-4$$

Add \frac{3}{2} to both sides.

$$\frac{13}{2}x=-4+\frac{3}{2}$$

Convert -4 to fraction -\frac{8}{2}.

$$\frac{13}{2}x=-\frac{8}{2}+\frac{3}{2}$$

Since -\frac{8}{2} and \frac{3}{2} have the same denominator, add them by adding their numerators.

$$\frac{13}{2}x=\frac{-8+3}{2}$$

Add -8 and 3 to get -5.

$$\frac{13}{2}x=-\frac{5}{2}$$

Multiply both sides by \frac{2}{13}, the reciprocal of \frac{13}{2}.

$$x=-\frac{5}{2}\times \frac{2}{13}$$

Multiply -\frac{5}{2} times \frac{2}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\times 2}{2\times 13}$$

Cancel out 2 in both numerator and denominator.

$$x=\frac{-5}{13}$$

Fraction \frac{-5}{13} can be rewritten as -\frac{5}{13} by extracting the negative sign.

$$x=-\frac{5}{13}$$