Solve x≤0 and x≥−4 and write the solution in interval notation. If there is no solution, type ∅.

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alejandroguerrero345 alejandroguerrero345

06-09-2022
Mathematics

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Solve x≤0 and x≥−4 and write the solution in interval notation. If there is no solution, type ∅.

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rafikiedu14 rafikiedu14 · Answer 1 · 2022-09-13T12:47:36-04:00

The answer is (-∞.∞).

Draw out a number line. Plot 0 and -4 on the number line.

Shade to the left of x = 0, and have a filled in circle at the endpoint. This is the graph of x≤0

Then graph x ≥−4 by plotting a filled in circle at -4, and shading to the right.

Note how the two graphs overlap to cover the entire real number line

So if we have x≤0 or x≥−4 then we're basically saying x is any real number. To write this in interval notation, we write (−∞,∞)

This is the interval from negative infinity to positive infinity (or just infinity). We exclude each endpoint because we can't actually reach infinity itself. Infinity is not a number. Infinity is a concept

Side note: if you change the "or" to "and", then the solution to x≤0 and x≥−4 would be [-4, 0][−4,0] to indicate the interval from x = -4 to x = 0, including both endpoints. This is the region where the two graphs overlap.

To know more about graphs

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