Solve 7-11/2a+(1/2a-51/2)=2a+3/4-(frac{1}{2}+frac{1}{2}a)

$$7 - 1 \frac { 1 } { 2 } a + ( \frac { 1 } { 2 } a - 5 \frac { 1 } { 2 } ) = 2 a + \frac { 3 } { 4 } - ( \frac { 1 } { 2 } + \frac { 1 } { 2 } a )$$

Solve for a

$$a=\frac{1}{2}=0.5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 2,4.

$$4\left(7-\frac{1\times 2+1}{2}a\right)+2a-2\left(5\times 2+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Multiply 1 and 2 to get 2.

$$4\left(7-\frac{2+1}{2}a\right)+2a-2\left(5\times 2+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Add 2 and 1 to get 3.

$$4\left(7-\frac{3}{2}a\right)+2a-2\left(5\times 2+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Use the distributive property to multiply 4 by 7-\frac{3}{2}a.

$$28+4\left(-\frac{3}{2}\right)a+2a-2\left(5\times 2+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

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

$$28+\frac{4\left(-3\right)}{2}a+2a-2\left(5\times 2+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Multiply 4 and -3 to get -12.

$$28+\frac{-12}{2}a+2a-2\left(5\times 2+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Divide -12 by 2 to get -6.

$$28-6a+2a-2\left(5\times 2+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Combine -6a and 2a to get -4a.

$$28-4a-2\left(5\times 2+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Multiply 5 and 2 to get 10.

$$28-4a-2\left(10+1\right)=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Add 10 and 1 to get 11.

$$28-4a-2\times 11=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Multiply -2 and 11 to get -22.

$$28-4a-22=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

Subtract 22 from 28 to get 6.

$$6-4a=8a+3-4\left(\frac{1}{2}+\frac{1}{2}a\right)$$

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

$$6-4a=8a+3-4\times \frac{1}{2}-4\times \frac{1}{2}a$$

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

$$6-4a=8a+3+\frac{-4}{2}-4\times \frac{1}{2}a$$

Divide -4 by 2 to get -2.

$$6-4a=8a+3-2-4\times \frac{1}{2}a$$

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

$$6-4a=8a+3-2+\frac{-4}{2}a$$

Divide -4 by 2 to get -2.

$$6-4a=8a+3-2-2a$$

Subtract 2 from 3 to get 1.

$$6-4a=8a+1-2a$$

Combine 8a and -2a to get 6a.

$$6-4a=6a+1$$

Subtract 6a from both sides.

$$6-4a-6a=1$$

Combine -4a and -6a to get -10a.

$$6-10a=1$$

Subtract 6 from both sides.

$$-10a=1-6$$

Subtract 6 from 1 to get -5.

$$-10a=-5$$

Divide both sides by -10.

$$a=\frac{-5}{-10}$$

Reduce the fraction \frac{-5}{-10} to lowest terms by extracting and canceling out -5.

$$a=\frac{1}{2}$$