Solve 11/5n-2+5/6leq1/30

$$1 \frac { 1 } { 5 } n - 2 + \frac { 5 } { 6 } \leq \frac { 1 } { 30 }$$

Solve for n

$$n\leq 1$$

Solution Steps

Multiply both sides of the equation by 30, the least common multiple of 5,6,30. Since 30 is positive, the inequality direction remains the same.

$$6\left(1\times 5+1\right)n-60+25\leq 1$$

Multiply 1 and 5 to get 5.

$$6\left(5+1\right)n-60+25\leq 1$$

Add 5 and 1 to get 6.

$$6\times 6n-60+25\leq 1$$

Multiply 6 and 6 to get 36.

$$36n-60+25\leq 1$$

Add -60 and 25 to get -35.

$$36n-35\leq 1$$

Add 35 to both sides.

$$36n\leq 1+35$$

Add 1 and 35 to get 36.

$$36n\leq 36$$

Divide both sides by 36. Since 36 is positive, the inequality direction remains the same.

$$n\leq \frac{36}{36}$$

Divide 36 by 36 to get 1.

$$n\leq 1$$