Solve 2400/x=3/2*3700/x+5

$$\frac { 2400 } { x } = \frac { 3 } { 2 } \times \frac { 3700 } { x + 5 }$$

Solve for x

$$x = \frac{80}{21} = 3\frac{17}{21} \approx 3.80952381$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -5,0 since division by zero is not defined. Multiply both sides of the equation by 2x\left(x+5\right), the least common multiple of x,2,x+5.

$$\left(2x+10\right)\times 2400=\frac{3}{2}\times 2x\times 3700$$

Use the distributive property to multiply 2x+10 by 2400.

$$4800x+24000=\frac{3}{2}\times 2x\times 3700$$

Multiply \frac{3}{2} and 2 to get 3.

$$4800x+24000=3x\times 3700$$

Multiply 3 and 3700 to get 11100.

$$4800x+24000=11100x$$

Subtract 11100x from both sides.

$$4800x+24000-11100x=0$$

Combine 4800x and -11100x to get -6300x.

$$-6300x+24000=0$$

Subtract 24000 from both sides. Anything subtracted from zero gives its negation.

$$-6300x=-24000$$

Divide both sides by -6300.

$$x=\frac{-24000}{-6300}$$

Reduce the fraction \frac{-24000}{-6300} to lowest terms by extracting and canceling out -300.

$$x=\frac{80}{21}$$