Answer: (-5, infinity)
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Step-by-step explanation:
Let's solve for x
-6 < 3x+9
-6-9 < 3x+9-9 ... subtract 9 from both sides
-15 < 3x
-15/3 < 3x/3 ... divide both sides by 3
-5 < x
-5 < x < infinity
The last step is valid because any number is smaller than positive infinity. Infinity is more of a concept than a number. It basically says "the right side of the interval goes on forever"
The compound inequality -5 < x < infinity converts to the interval notation (-5, infinity)
The use of curved parenthesis tell the reader "do not include the endpoint as part of the solution". So -5 is not part of the interval. Since we can't ever reach infinity, we also cannot include it as part of the solution set.