Solve 1/2-2x-1/x+1=7/2

$$\frac { 1 } { 2 } - \frac { 2 x - 1 } { x + 1 } = \frac { 7 } { 2 }$$

Solve for x

$$x=-\frac{2}{5}=-0.4$$

Steps for Solving Linear Equation

Variable x cannot be equal to -1 since division by zero is not defined. Multiply both sides of the equation by 2\left(x+1\right), the least common multiple of 2,x+1.

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

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

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

Use the distributive property to multiply 2x+2 by \frac{1}{2}.

$$x+1-2\left(2x-1\right)=7\left(x+1\right)$$

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

$$x+1-4x+2=7\left(x+1\right)$$

Combine x and -4x to get -3x.

$$-3x+1+2=7\left(x+1\right)$$

Add 1 and 2 to get 3.

$$-3x+3=7\left(x+1\right)$$

Use the distributive property to multiply 7 by x+1.

$$-3x+3=7x+7$$

Subtract 7x from both sides.

$$-3x+3-7x=7$$

Combine -3x and -7x to get -10x.

$$-10x+3=7$$

Subtract 3 from both sides.

$$-10x=7-3$$

Subtract 3 from 7 to get 4.

$$-10x=4$$

Divide both sides by -10.

$$x=\frac{4}{-10}$$

Reduce the fraction \frac{4}{-10} to lowest terms by extracting and canceling out 2.

$$x=-\frac{2}{5}$$