Solve 5/4k+31/2+11/12>21/12

$$\frac { 5 } { 4 } k + 3 \frac { 1 } { 2 } + 1 \frac { 1 } { 12 } > 2 \frac { 1 } { 12 }$$

Solve for k

$$k>-2$$

Solution Steps

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

$$15k+6\left(3\times 2+1\right)+1\times 12+1>2\times 12+1$$

Multiply 3 and 2 to get 6.

$$15k+6\left(6+1\right)+1\times 12+1>2\times 12+1$$

Add 6 and 1 to get 7.

$$15k+6\times 7+1\times 12+1>2\times 12+1$$

Multiply 6 and 7 to get 42.

$$15k+42+1\times 12+1>2\times 12+1$$

Multiply 1 and 12 to get 12.

$$15k+42+12+1>2\times 12+1$$

Add 42 and 12 to get 54.

$$15k+54+1>2\times 12+1$$

Add 54 and 1 to get 55.

$$15k+55>2\times 12+1$$

Multiply 2 and 12 to get 24.

$$15k+55>24+1$$

Add 24 and 1 to get 25.

$$15k+55>25$$

Subtract 55 from both sides.

$$15k>25-55$$

Subtract 55 from 25 to get -30.

$$15k>-30$$

Divide both sides by 15. Since 15 is positive, the inequality direction remains the same.

$$k>\frac{-30}{15}$$

Divide -30 by 15 to get -2.

$$k>-2$$