Solve 1-1/2-1/2+1/3/2=2*frac{1}{2}-frac{frac{1}{2}-4(a-3*frac{1}{2})}{3}

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

Solve for a

$$a = \frac{13}{8} = 1\frac{5}{8} = 1.625$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$6-3\left(\frac{1}{2}-\frac{\frac{1}{2}+1}{3}\right)=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Convert 1 to fraction \frac{2}{2}.

$$6-3\left(\frac{1}{2}-\frac{\frac{1}{2}+\frac{2}{2}}{3}\right)=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

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

$$6-3\left(\frac{1}{2}-\frac{\frac{1+2}{2}}{3}\right)=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Add 1 and 2 to get 3.

$$6-3\left(\frac{1}{2}-\frac{\frac{3}{2}}{3}\right)=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Express \frac{\frac{3}{2}}{3} as a single fraction.

$$6-3\left(\frac{1}{2}-\frac{3}{2\times 3}\right)=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Cancel out 3 in both numerator and denominator.

$$6-3\left(\frac{1}{2}-\frac{1}{2}\right)=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Subtract \frac{1}{2} from \frac{1}{2} to get 0.

$$6-3\times 0=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Multiply -3 and 0 to get 0.

$$6+0=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Add 6 and 0 to get 6.

$$6=12\times \frac{1}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Multiply 12 and \frac{1}{2} to get \frac{12}{2}.

$$6=\frac{12}{2}-2\left(\frac{1}{2}-4\left(a-3\times \frac{1}{2}\right)\right)$$

Divide 12 by 2 to get 6.

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

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

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

Use the distributive property to multiply -4 by a-\frac{3}{2}.

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

Express -4\left(-\frac{3}{2}\right) as a single fraction.

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

Multiply -4 and -3 to get 12.

$$6=6-2\left(\frac{1}{2}-4a+\frac{12}{2}\right)$$

Divide 12 by 2 to get 6.

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

Convert 6 to fraction \frac{12}{2}.

$$6=6-2\left(\frac{1}{2}-4a+\frac{12}{2}\right)$$

Since \frac{1}{2} and \frac{12}{2} have the same denominator, add them by adding their numerators.

$$6=6-2\left(\frac{1+12}{2}-4a\right)$$

Add 1 and 12 to get 13.

$$6=6-2\left(\frac{13}{2}-4a\right)$$

Use the distributive property to multiply -2 by \frac{13}{2}-4a.

$$6=6-2\times \frac{13}{2}+8a$$

Multiply -2 times \frac{13}{2}.

$$6=6-13+8a$$

Subtract 13 from 6 to get -7.

$$6=-7+8a$$

Swap sides so that all variable terms are on the left hand side.

$$-7+8a=6$$

Add 7 to both sides.

$$8a=6+7$$

Add 6 and 7 to get 13.

$$8a=13$$

Divide both sides by 8.

$$a=\frac{13}{8}$$