Solve 2+1/2-1/2a+3=a+1/4

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

Solve for a

$$a = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Steps for Solving Linear Equation

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

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

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

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

Add 4 and 1 to get 5.

$$\frac{5}{2}-\frac{1}{2}a+3=a+\frac{1}{4}$$

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

$$\frac{5}{2}-\frac{1}{2}a+\frac{6}{2}=a+\frac{1}{4}$$

Since \frac{5}{2} and \frac{6}{2} have the same denominator, add them by adding their numerators.

$$\frac{5+6}{2}-\frac{1}{2}a=a+\frac{1}{4}$$

Add 5 and 6 to get 11.

$$\frac{11}{2}-\frac{1}{2}a=a+\frac{1}{4}$$

Subtract a from both sides.

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

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

$$\frac{11}{2}-\frac{3}{2}a=\frac{1}{4}$$

Subtract \frac{11}{2} from both sides.

$$-\frac{3}{2}a=\frac{1}{4}-\frac{11}{2}$$

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

$$-\frac{3}{2}a=\frac{1}{4}-\frac{22}{4}$$

Since \frac{1}{4} and \frac{22}{4} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{3}{2}a=\frac{1-22}{4}$$

Subtract 22 from 1 to get -21.

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

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

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

Multiply -\frac{21}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$a=\frac{-21\left(-2\right)}{4\times 3}$$

Do the multiplications in the fraction \frac{-21\left(-2\right)}{4\times 3}.

$$a=\frac{42}{12}$$

Reduce the fraction \frac{42}{12} to lowest terms by extracting and canceling out 6.

$$a=\frac{7}{2}$$