Solve 13-7x/4-2/1=1/2alpha-(1/1-frac{2alpha+1}{4})

$$\frac { 13 - 7 x } { 4 } - \frac { 2 } { 1 } = \frac { 1 } { 2 } \alpha - ( \frac { 1 } { 1 } - \frac { 2 \alpha + 1 } { 4 } )$$

Solve for x

$$x=\frac{8-4\alpha }{7}$$

Steps for Solving Linear Equation

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

$$13-7x-4\times 2=2\alpha -4\left(\frac{1}{1}-\frac{2\alpha +1}{4}\right)$$

Multiply -4 and 2 to get -8.

$$13-7x-8=2\alpha -4\left(\frac{1}{1}-\frac{2\alpha +1}{4}\right)$$

Subtract 8 from 13 to get 5.

$$5-7x=2\alpha -4\left(\frac{1}{1}-\frac{2\alpha +1}{4}\right)$$

Anything divided by one gives itself.

$$5-7x=2\alpha -4\left(1-\frac{2\alpha +1}{4}\right)$$

Divide each term of 2\alpha +1 by 4 to get \frac{1}{2}\alpha +\frac{1}{4}.

$$5-7x=2\alpha -4\left(1-\left(\frac{1}{2}\alpha +\frac{1}{4}\right)\right)$$

To find the opposite of \frac{1}{2}\alpha +\frac{1}{4}, find the opposite of each term.

$$5-7x=2\alpha -4\left(1-\frac{1}{2}\alpha -\frac{1}{4}\right)$$

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$5-7x=2\alpha -4\left(\frac{3}{4}-\frac{1}{2}\alpha \right)$$

Use the distributive property to multiply -4 by \frac{3}{4}-\frac{1}{2}\alpha .

$$5-7x=2\alpha -3+2\alpha$$

Combine 2\alpha and 2\alpha to get 4\alpha .

$$5-7x=4\alpha -3$$

Subtract 5 from both sides.

$$-7x=4\alpha -3-5$$

Subtract 5 from -3 to get -8.

$$-7x=4\alpha -8$$

Divide both sides by -7.

$$\frac{-7x}{-7}=\frac{4\alpha -8}{-7}$$

Dividing by -7 undoes the multiplication by -7.

$$x=\frac{4\alpha -8}{-7}$$

Divide -8+4\alpha by -7.

$$x=\frac{8-4\alpha }{7}$$

Solve for α

$$\alpha =-\frac{7x}{4}+2$$

Steps for Solving Linear Equation

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

$$13-7x-4\times 2=2\alpha -4\left(\frac{1}{1}-\frac{2\alpha +1}{4}\right)$$

Multiply -4 and 2 to get -8.

$$13-7x-8=2\alpha -4\left(\frac{1}{1}-\frac{2\alpha +1}{4}\right)$$

Subtract 8 from 13 to get 5.

$$5-7x=2\alpha -4\left(\frac{1}{1}-\frac{2\alpha +1}{4}\right)$$

Anything divided by one gives itself.

$$5-7x=2\alpha -4\left(1-\frac{2\alpha +1}{4}\right)$$

Divide each term of 2\alpha +1 by 4 to get \frac{1}{2}\alpha +\frac{1}{4}.

$$5-7x=2\alpha -4\left(1-\left(\frac{1}{2}\alpha +\frac{1}{4}\right)\right)$$

To find the opposite of \frac{1}{2}\alpha +\frac{1}{4}, find the opposite of each term.

$$5-7x=2\alpha -4\left(1-\frac{1}{2}\alpha -\frac{1}{4}\right)$$

Subtract \frac{1}{4} from 1 to get \frac{3}{4}.

$$5-7x=2\alpha -4\left(\frac{3}{4}-\frac{1}{2}\alpha \right)$$

Use the distributive property to multiply -4 by \frac{3}{4}-\frac{1}{2}\alpha .

$$5-7x=2\alpha -3+2\alpha$$

Combine 2\alpha and 2\alpha to get 4\alpha .

$$5-7x=4\alpha -3$$

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

$$4\alpha -3=5-7x$$

Add 3 to both sides.

$$4\alpha =5-7x+3$$

Add 5 and 3 to get 8.

$$4\alpha =8-7x$$

Divide both sides by 4.

$$\frac{4\alpha }{4}=\frac{8-7x}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$\alpha =\frac{8-7x}{4}$$

Divide 8-7x by 4.

$$\alpha =-\frac{7x}{4}+2$$