Solve and graph the inequality -5a + 17 < 62

Answer 1

To solve the inequality -5a + 17 < 62, we can follow these steps:

Step 1: Subtract 17 from both sides of the inequality:
-5a + 17 - 17 < 62 - 17
-5a < 45

Step 2: Divide both sides of the inequality by -5. Since we are dividing by a negative number, we need to reverse the inequality sign:
(-5a)/-5 > 45/-5
a > -9

So, the solution to the inequality is a > -9.

To graph the inequality, we can draw a number line and shade the region to the right of -9 to represent all the values of a that satisfy the inequality.

Here is a graph of the inequality:

--------------------> (arrow pointing towards the right)
-9 (a value on the number line)

The shaded region to the right of -9 represents all the values of a that make the inequality -5a + 17 < 62 true.

Answer 2

do you graph that with an open circle or a closed circle on the number line?

Answer 3

Apologies for the oversight. Since the inequality is a > -9 (greater than), we would use an open circle on -9 to indicate that it is not included in the solution set.

Here is the corrected graph:

-------o------------------> (arrow pointing towards the right)
-9 (a open circle on -9 on the number line)

The open circle on -9 indicates that -9 is not included in the solution set.