Solve 2x/5+1/2=4x/9-4/5

$$\frac{ 2x }{ 5 } + \frac{ 1 }{ 2 } = \frac{ 4x }{ 9 } - \frac{ 4 }{ 5 }$$

Solve for x

$$x = \frac{117}{4} = 29\frac{1}{4} = 29.25$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 90, the least common multiple of 5,2,9.

$$18\times 2x+45=10\times 4x-72$$

Multiply 18 and 2 to get 36.

$$36x+45=10\times 4x-72$$

Multiply 10 and 4 to get 40.

$$36x+45=40x-72$$

Subtract 40x from both sides.

$$36x+45-40x=-72$$

Combine 36x and -40x to get -4x.

$$-4x+45=-72$$

Subtract 45 from both sides.

$$-4x=-72-45$$

Subtract 45 from -72 to get -117.

$$-4x=-117$$

Divide both sides by -4.

$$x=\frac{-117}{-4}$$

Fraction \frac{-117}{-4} can be simplified to \frac{117}{4} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{117}{4}$$