Solve x+5/3<1-3-2x/5

$$\frac{ x+5 }{ 3 } < 1- \frac{ 3-2x }{ 5 }$$

Solve for x

$$x>19$$

Solution Steps

Multiply both sides of the equation by 15, the least common multiple of 3,5. Since 15 is positive, the inequality direction remains the same.

$$5\left(x+5\right)<15-3\left(3-2x\right)$$

Use the distributive property to multiply 5 by x+5.

$$5x+25<15-3\left(3-2x\right)$$

Use the distributive property to multiply -3 by 3-2x.

$$5x+25<15-9+6x$$

Subtract 9 from 15 to get 6.

$$5x+25<6+6x$$

Subtract 6x from both sides.

$$5x+25-6x<6$$

Combine 5x and -6x to get -x.

$$-x+25<6$$

Subtract 25 from both sides.

$$-x<6-25$$

Subtract 25 from 6 to get -19.

$$-x<-19$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x>\frac{-19}{-1}$$

Fraction \frac{-19}{-1} can be simplified to 19 by removing the negative sign from both the numerator and the denominator.

$$x>19$$