Answer: (-infinity, 7]
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Explanation:
The first interval (-infinity, 3) describes any number less than 3, so we can write x < 3 in short hand (where x is the unknown number).
The second interval (-1, 7] means we start at -1 and stop at 7. We do not include -1 but include 7. So we say that [tex]-1 < x \le 7[/tex] (ie x is between -1 and 7; exclude -1, include 7)
If you were to graph each ona number line, you would see that the too intervals have overlapping parts. The right most edge extends out as far as x = 7. There is no left most edge as it goes onforever that direction.
Therefore, the to intervals combine to get [tex]x \le 7[/tex] which turns into the interval notation answer of (-infinity, 7]
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It might help to think of it like this: x < 3 and [tex]-1 < x \le 7[/tex] say "x is some number that is less than 3, or it is between -1 and 7". So x could be anything less than 7, including 7 itself.
