Solve 3x+x/2=4-2/x+7x/2

$$3 x + \frac { x } { 2 } = 4 - \frac { 2 } { x } + \frac { 7 x } { 2 }$$

Solve for x

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

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2x, the least common multiple of 2,x.

$$3x\times 2x+xx=2x\times 4-2\times 2+x\times 7x$$

Multiply x and x to get x^{2}.

$$3x\times 2x+x^{2}=2x\times 4-2\times 2+x\times 7x$$

Multiply 3 and 2 to get 6.

$$6xx+x^{2}=2x\times 4-2\times 2+x\times 7x$$

Multiply x and x to get x^{2}.

$$6x^{2}+x^{2}=2x\times 4-2\times 2+x\times 7x$$

Combine 6x^{2} and x^{2} to get 7x^{2}.

$$7x^{2}=2x\times 4-2\times 2+x\times 7x$$

Multiply x and x to get x^{2}.

$$7x^{2}=2x\times 4-2\times 2+x^{2}\times 7$$

Multiply 2 and 4 to get 8.

$$7x^{2}=8x-2\times 2+x^{2}\times 7$$

Multiply -2 and 2 to get -4.

$$7x^{2}=8x-4+x^{2}\times 7$$

Subtract 8x from both sides.

$$7x^{2}-8x=-4+x^{2}\times 7$$

Subtract x^{2}\times 7 from both sides.

$$7x^{2}-8x-x^{2}\times 7=-4$$

Combine 7x^{2} and -x^{2}\times 7 to get 0.

$$-8x=-4$$

Divide both sides by -8.

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

Reduce the fraction \frac{-4}{-8} to lowest terms by extracting and canceling out -4.

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