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

$$\frac { 1 } { 4 } ( x - 1 ) + \frac { 5 } { 2 } = \frac { 1 } { 6 } ( 3 - 2 x )$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by x-1.

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

Multiply \frac{1}{4} and -1 to get -\frac{1}{4}.

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

Least common multiple of 4 and 2 is 4. Convert -\frac{1}{4} and \frac{5}{2} to fractions with denominator 4.

$$\frac{1}{4}x-\frac{1}{4}+\frac{10}{4}=\frac{1}{6}\left(3-2x\right)$$

Since -\frac{1}{4} and \frac{10}{4} have the same denominator, add them by adding their numerators.

$$\frac{1}{4}x+\frac{-1+10}{4}=\frac{1}{6}\left(3-2x\right)$$

Add -1 and 10 to get 9.

$$\frac{1}{4}x+\frac{9}{4}=\frac{1}{6}\left(3-2x\right)$$

Use the distributive property to multiply \frac{1}{6} by 3-2x.

$$\frac{1}{4}x+\frac{9}{4}=\frac{1}{6}\times 3+\frac{1}{6}\left(-2\right)x$$

Multiply \frac{1}{6} and 3 to get \frac{3}{6}.

$$\frac{1}{4}x+\frac{9}{4}=\frac{3}{6}+\frac{1}{6}\left(-2\right)x$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{4}x+\frac{9}{4}=\frac{1}{2}+\frac{1}{6}\left(-2\right)x$$

Multiply \frac{1}{6} and -2 to get \frac{-2}{6}.

$$\frac{1}{4}x+\frac{9}{4}=\frac{1}{2}+\frac{-2}{6}x$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{1}{4}x+\frac{9}{4}=\frac{1}{2}-\frac{1}{3}x$$

Add \frac{1}{3}x to both sides.

$$\frac{1}{4}x+\frac{9}{4}+\frac{1}{3}x=\frac{1}{2}$$

Combine \frac{1}{4}x and \frac{1}{3}x to get \frac{7}{12}x.

$$\frac{7}{12}x+\frac{9}{4}=\frac{1}{2}$$

Subtract \frac{9}{4} from both sides.

$$\frac{7}{12}x=\frac{1}{2}-\frac{9}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{9}{4} to fractions with denominator 4.

$$\frac{7}{12}x=\frac{2}{4}-\frac{9}{4}$$

Since \frac{2}{4} and \frac{9}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{12}x=\frac{2-9}{4}$$

Subtract 9 from 2 to get -7.

$$\frac{7}{12}x=-\frac{7}{4}$$

Multiply both sides by \frac{12}{7}, the reciprocal of \frac{7}{12}.

$$x=-\frac{7}{4}\times \frac{12}{7}$$

Multiply -\frac{7}{4} times \frac{12}{7} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\times 12}{4\times 7}$$

Do the multiplications in the fraction \frac{-7\times 12}{4\times 7}.

$$x=\frac{-84}{28}$$

Divide -84 by 28 to get -3.

$$x=-3$$