Solve -4(y-6)leq(-9+y)(-2)

$$- 4 ( y - 6 ) \leq ( - 9 + y ) ( - 2 )$$

Solve for y

$$y\geq 3$$

Solution Steps

Use the distributive property to multiply -4 by y-6.

$$-4y+24\leq \left(-9+y\right)\left(-2\right)$$

Use the distributive property to multiply -9+y by -2.

$$-4y+24\leq 18-2y$$

Add 2y to both sides.

$$-4y+24+2y\leq 18$$

Combine -4y and 2y to get -2y.

$$-2y+24\leq 18$$

Subtract 24 from both sides.

$$-2y\leq 18-24$$

Subtract 24 from 18 to get -6.

$$-2y\leq -6$$

Divide both sides by -2. Since -2 is negative, the inequality direction is changed.

$$y\geq \frac{-6}{-2}$$

Divide -6 by -2 to get 3.

$$y\geq 3$$