Question

solve the inequality and graph the solution.
12 < \frac{k - 15}{-1}
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Multiply both sides by -1

When multiplying an inequality by a negative number, the inequality sign flips. So we get $12\times(- 1)>\frac{k - 15}{-1}\times(-1)$, which simplifies to $-12>k - 15$.

Step2: Add 15 to both sides

Adding 15 to both sides of the inequality $-12>k - 15$ gives $-12 + 15>k-15 + 15$. So, $3>k$ or $k < 3$.

Answer:

The solution of the inequality is $k < 3$. On the number - line, we use an open - circle at 3 (since 3 is not included in the solution) and draw an arrow to the left to represent all the values of $k$ that satisfy the inequality.