Solve 4+y/2-y+2/7<y+3

$$\frac { 4 + y } { 2 } - \frac { y + 2 } { 7 } < y + 3$$

Solve for y

$$y>-2$$

Solution Steps

Multiply both sides of the equation by 14, the least common multiple of 2,7. Since 14 is positive, the inequality direction remains the same.

$$7\left(4+y\right)-2\left(y+2\right)<14y+42$$

Use the distributive property to multiply 7 by 4+y.

$$28+7y-2\left(y+2\right)<14y+42$$

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

$$28+7y-2y-4<14y+42$$

Combine 7y and -2y to get 5y.

$$28+5y-4<14y+42$$

Subtract 4 from 28 to get 24.

$$24+5y<14y+42$$

Subtract 14y from both sides.

$$24+5y-14y<42$$

Combine 5y and -14y to get -9y.

$$24-9y<42$$

Subtract 24 from both sides.

$$-9y<42-24$$

Subtract 24 from 42 to get 18.

$$-9y<18$$

Divide both sides by -9. Since -9 is negative, the inequality direction is changed.

$$y>\frac{18}{-9}$$

Divide 18 by -9 to get -2.

$$y>-2$$