Solve y+2.51-y/60/frac{1{30}}leq64

$$y+2.5 \frac{ 1- \frac{ y }{ 60 } }{ \frac{ 1 }{ 30 } } \leq 64$$

Solve for y

$$y\geq 44$$

Solution Steps

Divide each term of 1-\frac{y}{60} by \frac{1}{30} to get \frac{1}{\frac{1}{30}}+\frac{-\frac{y}{60}}{\frac{1}{30}}.

$$y+2.5\left(\frac{1}{\frac{1}{30}}+\frac{-\frac{y}{60}}{\frac{1}{30}}\right)\leq 64$$

Divide 1 by \frac{1}{30} by multiplying 1 by the reciprocal of \frac{1}{30}.

$$y+2.5\left(1\times 30+\frac{-\frac{y}{60}}{\frac{1}{30}}\right)\leq 64$$

Multiply 1 and 30 to get 30.

$$y+2.5\left(30+\frac{-\frac{y}{60}}{\frac{1}{30}}\right)\leq 64$$

Use the distributive property to multiply 2.5 by 30+\frac{-\frac{y}{60}}{\frac{1}{30}}.

$$y+75+2.5\times \frac{-\frac{y}{60}}{\frac{1}{30}}\leq 64$$

Subtract 75 from both sides.

$$y+2.5\times \frac{-\frac{y}{60}}{\frac{1}{30}}\leq 64-75$$

Subtract 75 from 64 to get -11.

$$y+2.5\times \frac{-\frac{y}{60}}{\frac{1}{30}}\leq -11$$

Divide -\frac{y}{60} by \frac{1}{30} to get -30\times \frac{y}{60}.

$$y+2.5\left(-30\right)\times \frac{y}{60}\leq -11$$

Multiply 2.5 and -30 to get -75.

$$y-75\times \frac{y}{60}\leq -11$$

Express -75\times \frac{y}{60} as a single fraction.

$$y+\frac{-75y}{60}\leq -11$$

Divide -75y by 60 to get -\frac{5}{4}y.

$$y-\frac{5}{4}y\leq -11$$

Combine y and -\frac{5}{4}y to get -\frac{1}{4}y.

$$-\frac{1}{4}y\leq -11$$

Multiply both sides by -4, the reciprocal of -\frac{1}{4}. Since -\frac{1}{4} is negative, the inequality direction is changed.

$$y\geq -11\left(-4\right)$$

Multiply -11 and -4 to get 44.

$$y\geq 44$$