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

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

Solve for x

$$x = -\frac{9}{2} = -4\frac{1}{2} = -4.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{1}{4} by 2x-1.

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

Multiply \frac{1}{4} and 2 to get \frac{2}{4}.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

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

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

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

Convert 3 to fraction \frac{12}{4}.

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

Since -\frac{1}{4} and \frac{12}{4} have the same denominator, add them by adding their numerators.

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

Add -1 and 12 to get 11.

$$\frac{1}{2}x+\frac{11}{4}=\frac{1}{2}$$

Subtract \frac{11}{4} from both sides.

$$\frac{1}{2}x=\frac{1}{2}-\frac{11}{4}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{11}{4} to fractions with denominator 4.

$$\frac{1}{2}x=\frac{2}{4}-\frac{11}{4}$$

Since \frac{2}{4} and \frac{11}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x=\frac{2-11}{4}$$

Subtract 11 from 2 to get -9.

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

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=-\frac{9}{4}\times 2$$

Express -\frac{9}{4}\times 2 as a single fraction.

$$x=\frac{-9\times 2}{4}$$

Multiply -9 and 2 to get -18.

$$x=\frac{-18}{4}$$

Reduce the fraction \frac{-18}{4} to lowest terms by extracting and canceling out 2.

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