Question
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Answer
There are no solutions; the solution set is empty.
Solution
We start with the inequality:
|9w – 6| + 9 ≤ 2
Subtract 9 from both sides:
|9w – 6| ≤ 2 – 9
|9w – 6| ≤ -7
Since absolute value expressions are always nonnegative (|9w – 6| ≥ 0), they cannot be less than or equal to -7. Therefore, there are no values of w that satisfy this inequality.
The solution set is the empty set.
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Simplify this solution Mind Expander
To solve the inequality \( |9w - 6| + 9 \leq 2 \), first, isolate the absolute value: \[ |9w - 6| \leq 2 - 9 \] This simplifies to: \[ |9w - 6| \leq -7 \] Since an absolute value cannot be negative, there are no solutions to this inequality. The solution set is therefore empty. But emotions can be complex, just like solving inequalities! Just remember to check if isolating the absolute value leads to a non-negative result; if it doesn't, you're likely dealing with no solutions. It's like trying to find a unicorn in a desert—sometimes, the quest is just as enlightening as finding the treasure!
