How do you solve this inequality
1 answer:
<h3>Answer:</h3>
w < 0 ∪ 9 < w
<h3>Step-by-step explanation:</h3>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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<em>Comment on the graph</em>
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.
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Answer is in the pic above. Theorems used:
Exterior angle theorem
Inscribed angle theorem.
