Solve x+1/2*(x-1/2)=2x-1/4(x+2)+15/4

$$\frac { x + 1 } { 2 } \cdot ( x - \frac { 1 } { 2 } ) = \frac { 2 x - 1 } { 4 } ( x + 2 ) + \frac { 15 } { 4 }$$

Solve for x

$$x=-7$$

Steps for Solving Linear Equation

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

$$2\left(x+1\right)\left(x-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Use the distributive property to multiply 2 by x+1.

$$\left(2x+2\right)\left(x-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Apply the distributive property by multiplying each term of 2x+2 by each term of x-\frac{1}{2}.

$$2x^{2}+2x\left(-\frac{1}{2}\right)+2x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Cancel out 2 and 2.

$$2x^{2}-x+2x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Combine -x and 2x to get x.

$$2x^{2}+x+2\left(-\frac{1}{2}\right)=\left(2x-1\right)\left(x+2\right)+15$$

Cancel out 2 and 2.

$$2x^{2}+x-1=\left(2x-1\right)\left(x+2\right)+15$$

Apply the distributive property by multiplying each term of 2x-1 by each term of x+2.

$$2x^{2}+x-1=2x^{2}+4x-x-2+15$$

Combine 4x and -x to get 3x.

$$2x^{2}+x-1=2x^{2}+3x-2+15$$

Add -2 and 15 to get 13.

$$2x^{2}+x-1=2x^{2}+3x+13$$

Subtract 2x^{2} from both sides.

$$2x^{2}+x-1-2x^{2}=3x+13$$

Combine 2x^{2} and -2x^{2} to get 0.

$$x-1=3x+13$$

Subtract 3x from both sides.

$$x-1-3x=13$$

Combine x and -3x to get -2x.

$$-2x-1=13$$

Add 1 to both sides.

$$-2x=13+1$$

Add 13 and 1 to get 14.

$$-2x=14$$

Divide both sides by -2.

$$x=\frac{14}{-2}$$

Divide 14 by -2 to get -7.

$$x=-7$$