Question

Which number line shows the solution to the inequality 5x - 15 > -65

A.
The number line shows numbers from -12 to -8. There is a open circle at -10, a bold line from -10 heading to its left.

B.
The number line shows numbers from -12 to -8. There is a closed circle at -10, a bold line from -10 heading to its left.

C.
The number line shows numbers from -12 to -8. There is a open circle at -10, a bold line from -10 heading rightwards.

D.
The number line shows numbers from -12 to -8. There is a closed circle at -10, a bold line from -10 heading rightwards.

Answer 1

To solve the inequality \( 5x - 15 > -65 \), we first isolate \( x \) by adding 15 to both sides:

\[
5x > -65 + 15
\]

\[
5x > -50
\]

Next, we divide both sides by 5:

\[
x > -10
\]

Now, we interpret this solution. The inequality \( x > -10 \) means that \( x \) can be any number greater than \(-10\).

In terms of a number line representation:
- We place an **open circle** at \(-10\) indicating that \(-10\) is **not included** in the solution.
- We draw a **bold line** extending to the right from \(-10\) to indicate all numbers greater than \(-10\).

Therefore, the correct representation of the solution on a number line is:

**C. The number line shows numbers from -12 to -8. There is an open circle at -10, a bold line from -10 heading rightwards.**