Solve 3(2+y)-2(3-y)leqy

$$3 ( 2 + y ) - 2 ( 3 - y ) \leq y$$

Solve for y

$$y\leq 0$$

Solution Steps

Use the distributive property to multiply 3 by 2+y.

$$6+3y-2\left(3-y\right)\leq y$$

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

$$6+3y-6+2y\leq y$$

Subtract 6 from 6 to get 0.

$$3y+2y\leq y$$

Combine 3y and 2y to get 5y.

$$5y\leq y$$

Subtract y from both sides.

$$5y-y\leq 0$$

Combine 5y and -y to get 4y.

$$4y\leq 0$$

Product of two numbers is ≤0 if one is ≥0 and the other is ≤0. Since 4\geq 0, y must be ≤0.

$$y\leq 0$$