How do you solve and graph #k+3/4>1/3#?

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the right side of the line because the inequality operator has a "greater than" clause:

graph{x>=-5/12 [-2, 2, -1, 1]}

To solve and graph the inequality ( \frac{k + 3}{4} > \frac{1}{3} ), follow these steps:

1. Multiply both sides of the inequality by 4 to eliminate the fraction: ( 4 \cdot \frac{k + 3}{4} > 4 \cdot \frac{1}{3} )

2. Simplify: ( k + 3 > \frac{4}{3} )

3. Subtract 3 from both sides of the inequality: ( k + 3 - 3 > \frac{4}{3} - 3 ) ( k > \frac{4}{3} - 3 )

4. Simplify: ( k > \frac{4}{3} - \frac{9}{3} ) ( k > \frac{-5}{3} )

5. Graph the solution on a number line, indicating that ( k ) is greater than ( -\frac{5}{3} ).

6. Use an open circle to represent that ( k ) is not equal to ( -\frac{5}{3} ), since the inequality is strict.

7. Shade the region to the right of ( -\frac{5}{3} ) to show all values of ( k ) that satisfy the inequality.