Solve 1/2(x-1)+2=3(2x-1)

$$\frac { 1 } { 2 } ( x - 1 ) + 2 = 3 ( 2 x - 1 )$$

Solve for x

$$x=\frac{9}{11}\approx 0.818181818$$

Steps for Solving Linear Equation

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

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

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

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

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

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

Since -\frac{1}{2} and \frac{4}{2} have the same denominator, add them by adding their numerators.

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

Add -1 and 4 to get 3.

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

Use the distributive property to multiply 3 by 2x-1.

$$\frac{1}{2}x+\frac{3}{2}=6x-3$$

Subtract 6x from both sides.

$$\frac{1}{2}x+\frac{3}{2}-6x=-3$$

Combine \frac{1}{2}x and -6x to get -\frac{11}{2}x.

$$-\frac{11}{2}x+\frac{3}{2}=-3$$

Subtract \frac{3}{2} from both sides.

$$-\frac{11}{2}x=-3-\frac{3}{2}$$

Convert -3 to fraction -\frac{6}{2}.

$$-\frac{11}{2}x=-\frac{6}{2}-\frac{3}{2}$$

Since -\frac{6}{2} and \frac{3}{2} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{11}{2}x=\frac{-6-3}{2}$$

Subtract 3 from -6 to get -9.

$$-\frac{11}{2}x=-\frac{9}{2}$$

Multiply both sides by -\frac{2}{11}, the reciprocal of -\frac{11}{2}.

$$x=-\frac{9}{2}\left(-\frac{2}{11}\right)$$

Multiply -\frac{9}{2} times -\frac{2}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-9\left(-2\right)}{2\times 11}$$

Do the multiplications in the fraction \frac{-9\left(-2\right)}{2\times 11}.

$$x=\frac{18}{22}$$

Reduce the fraction \frac{18}{22} to lowest terms by extracting and canceling out 2.

$$x=\frac{9}{11}$$