Solve .5-3Y+9-Y-4Y-7+4+3Y<0

$$.5 - 3 Y + 9 - Y - 4 Y - 7 + 4 + 3 Y < 0$$

Solve for Y

$$Y>\frac{13}{10}$$

Solution Steps

Add 0.5 and 9 to get 9.5.

$$9.5-3Y-Y-4Y-7+4+3Y<0$$

Combine -3Y and -Y to get -4Y.

$$9.5-4Y-4Y-7+4+3Y<0$$

Combine -4Y and -4Y to get -8Y.

$$9.5-8Y-7+4+3Y<0$$

Subtract 7 from 9.5 to get 2.5.

$$2.5-8Y+4+3Y<0$$

Add 2.5 and 4 to get 6.5.

$$6.5-8Y+3Y<0$$

Combine -8Y and 3Y to get -5Y.

$$6.5-5Y<0$$

Subtract 6.5 from both sides. Anything subtracted from zero gives its negation.

$$-5Y<-6.5$$

Divide both sides by -5. Since -5 is negative, the inequality direction is changed.

$$Y>\frac{-6.5}{-5}$$

Expand \frac{-6.5}{-5} by multiplying both numerator and the denominator by 10.

$$Y>\frac{-65}{-50}$$

Reduce the fraction \frac{-65}{-50} to lowest terms by extracting and canceling out -5.

$$Y>\frac{13}{10}$$