Solve y+1/3-y-1/2geqy-1/6

$$\frac{ y+1 }{ 3 } - \frac{ y-1 }{ 2 } \geq \frac{ y-1 }{ 6 }$$

Solve for y

$$y\leq 3$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2,6. Since 6 is positive, the inequality direction remains the same.

$$2\left(y+1\right)-3\left(y-1\right)\geq y-1$$

Use the distributive property to multiply 2 by y+1.

$$2y+2-3\left(y-1\right)\geq y-1$$

Use the distributive property to multiply -3 by y-1.

$$2y+2-3y+3\geq y-1$$

Combine 2y and -3y to get -y.

$$-y+2+3\geq y-1$$

Add 2 and 3 to get 5.

$$-y+5\geq y-1$$

Subtract y from both sides.

$$-y+5-y\geq -1$$

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

$$-2y+5\geq -1$$

Subtract 5 from both sides.

$$-2y\geq -1-5$$

Subtract 5 from -1 to get -6.

$$-2y\geq -6$$

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

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

Divide -6 by -2 to get 3.

$$y\leq 3$$