Question

Which number line represents the solution to 6+9r > 51

Answer 1

Answer:

The inequality solves to r > 5

The graph has an open hole at 5, with shading to the right

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Explanation:

6+9r is the same as 9r+6

We'll subtract 6 from both sides to undo the +6

9r+6 > 51

9r+6-6 > 51-6

9r > 45

Then we'll divide both sides by 9 to isolate r.

9r/9 > 45/9

r > 5

The entire time, the inequality sign stays the same.

The solution set involves anything larger than 5. So something like r = 7 would work while r = 2 does not.

Visually, we'll have an open hole at 5 on the number line. Shade to the right to indicate things larger than 5. The open hole tells the reader "do not include 5 as part of the solution set".