Solve 5y-1/-3<7(y+1)/-2

$$\frac { 5 y - 1 } { - 3 } < \frac { 7 ( y + 1 ) } { - 2 }$$

Solve for y

$$y<-\frac{23}{11}$$

Solution Steps

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

$$-2\left(5y-1\right)<-3\times 7\left(y+1\right)$$

Use the distributive property to multiply -2 by 5y-1.

$$-10y+2<-3\times 7\left(y+1\right)$$

Multiply -3 and 7 to get -21.

$$-10y+2<-21\left(y+1\right)$$

Use the distributive property to multiply -21 by y+1.

$$-10y+2<-21y-21$$

Add 21y to both sides.

$$-10y+2+21y<-21$$

Combine -10y and 21y to get 11y.

$$11y+2<-21$$

Subtract 2 from both sides.

$$11y<-21-2$$

Subtract 2 from -21 to get -23.

$$11y<-23$$

Divide both sides by 11. Since 11 is positive, the inequality direction remains the same.

$$y<-\frac{23}{11}$$