Solve 2y+1/15-3geq4/5+y-y/3

$$\frac { 2 y + 1 } { 15 } - 3 \geq \frac { 4 } { 5 } + y - \frac { y } { 3 }$$

Solve for y

$$y\leq -7$$

Solution Steps

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

$$2y+1-45\geq 12+15y-5y$$

Subtract 45 from 1 to get -44.

$$2y-44\geq 12+15y-5y$$

Combine 15y and -5y to get 10y.

$$2y-44\geq 12+10y$$

Subtract 10y from both sides.

$$2y-44-10y\geq 12$$

Combine 2y and -10y to get -8y.

$$-8y-44\geq 12$$

Add 44 to both sides.

$$-8y\geq 12+44$$

Add 12 and 44 to get 56.

$$-8y\geq 56$$

Divide both sides by -8. Since -8 is negative, the inequality direction is changed.

$$y\leq \frac{56}{-8}$$

Divide 56 by -8 to get -7.

$$y\leq -7$$