Question

Write the following as an inequality.

- 2 is less than w, and 6 is greater than or equal to w
Use w only once in your inequality.​

Answer 1

-2 < w ≤ 6

Explanation:

The inequalities you're asked to combine are ...

-2 < w

6 ≥ w

Turn one of these around so the "arrows" point in the same direction. (My preference is that they point to the left.) Now you have ...

-2 < w

w ≤ 6

You combine these by putting w in the middle:

-2 < w ≤ 6

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Alternate solution

I like the above solution because it puts the components of the expression in the same (left-right) order as they appear on a number line. However, both inequalities can be turned around to get ...

6 ≥ w > -2