Solve 3*8+x/570000+x>2*5

$$\frac{ 3 \cdot 8+x }{ 570000+x } > 2 \cdot 5$$

Solve for x

$$x\in \left(-\frac{1899992}{3},-570000\right)$$

Solution Steps

Multiply 3 and 8 to get 24.

$$\frac{24+x}{570000+x}>2\times 5$$

Multiply 2 and 5 to get 10.

$$\frac{24+x}{570000+x}>10$$

Denominator 570000+x cannot be zero since division by zero is not defined. There are two cases.

$$570000+x>0 570000+x<0$$

Consider the case when 570000+x is positive. Move 570000 to the right hand side.

$$x>-570000$$

The initial inequality does not change the direction when multiplied by 570000+x for 570000+x>0.

$$24+x>10\left(570000+x\right)$$

Multiply out the right hand side.

$$24+x>5700000+10x$$

Move the terms containing x to the left hand side and all other terms to the right hand side.

$$x-10x>-24+5700000$$

Combine like terms.

$$-9x>5699976$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x<-\frac{1899992}{3}$$

Consider condition x>-570000 specified above.

$$x\in \emptyset$$

Now consider the case when 570000+x is negative. Move 570000 to the right hand side.

$$x<-570000$$

The initial inequality changes the direction when multiplied by 570000+x for 570000+x<0.

$$24+x<10\left(570000+x\right)$$

Multiply out the right hand side.

$$24+x<5700000+10x$$

Move the terms containing x to the left hand side and all other terms to the right hand side.

$$x-10x<-24+5700000$$

Combine like terms.

$$-9x<5699976$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$x>-\frac{1899992}{3}$$

Consider condition x<-570000 specified above.

$$x\in \left(-\frac{1899992}{3},-570000\right)$$

The final solution is the union of the obtained solutions.

$$x\in \left(-\frac{1899992}{3},-570000\right)$$