Question

solve the following inequality.
6.3r < -45.36
which graph shows the correct solution?
options with number lines: first set from -77 to -67, second same range, third from -7.7 to -6.8, fourth same range as third.

Explanation:

Step1: Solve the inequality

To solve \(6.3r < -45.36\), divide both sides by \(6.3\):
\(r < \frac{-45.36}{6.3}\)
Calculate \(\frac{-45.36}{6.3} = -7.2\). So the solution is \(r < -7.2\).

Step2: Analyze the number lines

• The first two number lines have values like \(-77, -76, \dots\), which are too large (incorrect scale).
• The third and fourth have a scale with \(-7.7, -7.6, \dots\), matching the solution’s magnitude.
• For \(r < -7.2\), the graph should have an open circle at \(-7.2\) (since \(r\) is not equal to \(-7.2\)) and an arrow pointing left (for values less than \(-7.2\)). The fourth graph has the open circle at \(-7.2\) and the arrow left, matching \(r < -7.2\).

Answer:

The fourth graph (the one with the open circle at -7.2 and the arrow pointing to the left, with the number line labeled -7.7, -7.6, ..., -6.8)