Question

How do you solve this inequality

Answer 1

Answer:

w < 0 ∪ 9 < w

Step-by-step explanation:

You can multiply by w to eliminate the fractions. This gives rise to two cases, one for w > 0, and one for w < 0.

For w > 0

In this case, the multiplier is positive, so the sense of the inequality remains unchanged. The inequality becomes ...

... 2 +3w > 29

... 3w > 27 . . . . subtract 2

... w > 9 . . . . . . divide by 3 (again, a positive number)

For w < 0

Multiplying an inequality by a negative number reverses the sense of the comparison. This gives us ...

... 2 +3w < 29

... 3w < 27 . . . . . . subtract 2

... w < 9 . . . . . . . . divide by 3 (a positive number)

The solution to this inequality is the intersection of this condition with the condition that w < 0. That will be ...

... w < 0

Solution

So, the solution to the given inequality is ...

... w < 0 ∪ 9 < w

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Comment on the graph

We have rewritten the inequality to the form ...

... 2/w +3 -29/w > 0 . . . . . . subtract the right side

The graphing calculator has plotted the curve represented by the left side of this inequality. The blue highlighting shows where that is greater than zero.