Solve 4/4+frac{2{x}}=0.24

$$\frac { 4 } { 4 + \frac { 2 } { x } } = 0.24$$

Solve for x

$$x=\frac{3}{19}\approx 0.157894737$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Multiply 4 times \frac{x}{x}.

$$\frac{4}{\frac{4x}{x}+\frac{2}{x}}=0.24$$

Since \frac{4x}{x} and \frac{2}{x} have the same denominator, add them by adding their numerators.

$$\frac{4}{\frac{4x+2}{x}}=0.24$$

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

$$\frac{4x}{4x+2}=0.24$$

Factor the expressions that are not already factored in \frac{4x}{4x+2}.

$$\frac{4x}{2\left(2x+1\right)}=0.24$$

Cancel out 2 in both numerator and denominator.

$$\frac{2x}{2x+1}=0.24$$

Variable x cannot be equal to -\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by 2x+1.

$$2x=0.24\left(2x+1\right)$$

Use the distributive property to multiply 0.24 by 2x+1.

$$2x=0.48x+0.24$$

Subtract 0.48x from both sides.

$$2x-0.48x=0.24$$

Combine 2x and -0.48x to get 1.52x.

$$1.52x=0.24$$

Divide both sides by 1.52.

$$x=\frac{0.24}{1.52}$$

Expand \frac{0.24}{1.52} by multiplying both numerator and the denominator by 100.

$$x=\frac{24}{152}$$

Reduce the fraction \frac{24}{152} to lowest terms by extracting and canceling out 8.

$$x=\frac{3}{19}$$