Pregunta
Solución de inteligencia artificial de Upstudy
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Solución
To solve for
given the system of inequalities:
Let’s analyze each inequality step by step.
1. Solving
:
Result:
2. Other Inequalities:
-
-
-
(from above) -
3. Combining All Inequalities:
To find the solution that satisfies all the inequalities simultaneously, identify the most restrictive condition. Here’s how they stack up:
-
: Any less than 6. -
: More restrictive; must be less than -6. -
: Already covered by . -
: Also covered by .
The most restrictive condition here is
, as it ensures all other inequalities are also satisfied.
Final Solution:
Interpretation: The value of
must be less than -6 to satisfy all the given inequalities.
Respondido por UpStudy AI y revisado por un tutor profesional
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Extra Insights
Let’s tackle the inequalities step by step!
First inequality:
To solve it, we’ll rearrange it:
This simplifies to:
Dividing both sides by 2 gives:
The second inequality is:
The third inequality:
The fourth inequality states:
The fifth inequality is:
Now let’s combine these inequalities. The strictest condition here is
because it is more limiting than
and
. The main solution that satisfies all of these inequalities is:
To sum it up, the solution for
is
.
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