Solve x+x+4/frac{x{5}+x+4/10}=7

$$\frac { x + x + 4 } { \frac { x } { 5 } + \frac { x + 4 } { 10 } } = 7$$

Solve for x

$$x=12$$

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$\frac{2x+4}{\frac{x}{5}+\frac{x+4}{10}}=7$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 10 is 10. Multiply \frac{x}{5} times \frac{2}{2}.

$$\frac{2x+4}{\frac{2x}{10}+\frac{x+4}{10}}=7$$

Since \frac{2x}{10} and \frac{x+4}{10} have the same denominator, add them by adding their numerators.

$$\frac{2x+4}{\frac{2x+x+4}{10}}=7$$

Combine like terms in 2x+x+4.

$$\frac{2x+4}{\frac{3x+4}{10}}=7$$

Divide 2x+4 by \frac{3x+4}{10} by multiplying 2x+4 by the reciprocal of \frac{3x+4}{10}.

$$\frac{\left(2x+4\right)\times 10}{3x+4}=7$$

Use the distributive property to multiply 2x+4 by 10.

$$\frac{20x+40}{3x+4}=7$$

Variable x cannot be equal to -\frac{4}{3} since division by zero is not defined. Multiply both sides of the equation by 3x+4.

$$20x+40=7\left(3x+4\right)$$

Use the distributive property to multiply 7 by 3x+4.

$$20x+40=21x+28$$

Subtract 21x from both sides.

$$20x+40-21x=28$$

Combine 20x and -21x to get -x.

$$-x+40=28$$

Subtract 40 from both sides.

$$-x=28-40$$

Subtract 40 from 28 to get -12.

$$-x=-12$$

Multiply both sides by -1.

$$x=12$$