Solve 3+1/2+4{3+frac{2/x}}=4

$$3 + \frac { 1 } { 2 + \frac { 4 } { 3 + \frac { 2 } { x } } } = 4$$

Solve for x

$$x=-\frac{2}{7}\approx -0.285714286$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{x}{x}.

$$3+\frac{1}{2+\frac{4}{\frac{3x}{x}+\frac{2}{x}}}=4$$

Since \frac{3x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

$$3+\frac{1}{2+\frac{4}{\frac{3x+2}{x}}}=4$$

Variable x cannot be equal to 0 since division by zero is not defined. Divide 4 by \frac{3x+2}{x} by multiplying 4 by the reciprocal of \frac{3x+2}{x}.

$$3+\frac{1}{2+\frac{4x}{3x+2}}=4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{3x+2}{3x+2}.

$$3+\frac{1}{\frac{2\left(3x+2\right)}{3x+2}+\frac{4x}{3x+2}}=4$$

Since \frac{2\left(3x+2\right)}{3x+2} and \frac{4x}{3x+2} have the same denominator, add them by adding their numerators.

$$3+\frac{1}{\frac{2\left(3x+2\right)+4x}{3x+2}}=4$$

Do the multiplications in 2\left(3x+2\right)+4x.

$$3+\frac{1}{\frac{6x+4+4x}{3x+2}}=4$$

Combine like terms in 6x+4+4x.

$$3+\frac{1}{\frac{10x+4}{3x+2}}=4$$

Variable x cannot be equal to -\frac{2}{3} since division by zero is not defined. Divide 1 by \frac{10x+4}{3x+2} by multiplying 1 by the reciprocal of \frac{10x+4}{3x+2}.

$$3+\frac{3x+2}{10x+4}=4$$

Factor 10x+4.

$$3+\frac{3x+2}{2\left(5x+2\right)}=4$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2\left(5x+2\right)}{2\left(5x+2\right)}.

$$\frac{3\times 2\left(5x+2\right)}{2\left(5x+2\right)}+\frac{3x+2}{2\left(5x+2\right)}=4$$

Since \frac{3\times 2\left(5x+2\right)}{2\left(5x+2\right)} and \frac{3x+2}{2\left(5x+2\right)} have the same denominator, add them by adding their numerators.

$$\frac{3\times 2\left(5x+2\right)+3x+2}{2\left(5x+2\right)}=4$$

Do the multiplications in 3\times 2\left(5x+2\right)+3x+2.

$$\frac{30x+12+3x+2}{2\left(5x+2\right)}=4$$

Combine like terms in 30x+12+3x+2.

$$\frac{33x+14}{2\left(5x+2\right)}=4$$

Use the distributive property to multiply 2 by 5x+2.

$$\frac{33x+14}{10x+4}=4$$

Variable x cannot be equal to -\frac{2}{5} since division by zero is not defined. Multiply both sides of the equation by 2\left(5x+2\right).

$$33x+14=8\left(5x+2\right)$$

Use the distributive property to multiply 8 by 5x+2.

$$33x+14=40x+16$$

Subtract 40x from both sides.

$$33x+14-40x=16$$

Combine 33x and -40x to get -7x.

$$-7x+14=16$$

Subtract 14 from both sides.

$$-7x=16-14$$

Subtract 14 from 16 to get 2.

$$-7x=2$$

Divide both sides by -7.

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

Fraction \frac{2}{-7} can be rewritten as -\frac{2}{7} by extracting the negative sign.

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