Solve n+3/2-1leq3n/4+5/6

$$\frac { n + 3 } { 2 } - 1 \leq \frac { 3 n } { 4 } + \frac { 5 } { 6 }$$

Solve for n

$$n\geq -\frac{4}{3}$$

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 2,4,6. Since 12 is positive, the inequality direction remains the same.

$$6\left(n+3\right)-12\leq 3\times 3n+10$$

Use the distributive property to multiply 6 by n+3.

$$6n+18-12\leq 3\times 3n+10$$

Subtract 12 from 18 to get 6.

$$6n+6\leq 3\times 3n+10$$

Multiply 3 and 3 to get 9.

$$6n+6\leq 9n+10$$

Subtract 9n from both sides.

$$6n+6-9n\leq 10$$

Combine 6n and -9n to get -3n.

$$-3n+6\leq 10$$

Subtract 6 from both sides.

$$-3n\leq 10-6$$

Subtract 6 from 10 to get 4.

$$-3n\leq 4$$

Divide both sides by -3. Since -3 is negative, the inequality direction is changed.

$$n\geq -\frac{4}{3}$$