Which number line best represents the solution to the inequality 3.3w  9 > 22.27?
Understand the Problem
The question is asking to find the correct number line representation for the solution of the inequality 3.3w  9 > 22.27. To solve this, we first need to simplify the inequality and determine the range of values for w.
Answer
The solution is $w > 9.47$.
Answer for screen readers
The solution to the inequality is $w > 9.47$.
Steps to Solve

Simplify the inequality
Start with the original inequality: $$ 3.3w  9 > 22.27 $$
Next, add 9 to both sides to isolate the term with $w$: $$ 3.3w > 22.27 + 9 $$
This simplifies to: $$ 3.3w > 31.27 $$

Solve for $w$
Now, divide both sides by 3.3 to find $w$: $$ w > \frac{31.27}{3.3} $$
Calculating the division gives: $$ w > 9.47 $$

Determine the number line representation
The solution indicates that $w$ can take any value greater than 9.47. Therefore, on the number line, you'll have an open circle at 9.47 and a line extending to the right, indicating all values greater than 9.47.
The solution to the inequality is $w > 9.47$.
More Information
The value 9.47 is significant as it represents a threshold that $w$ must exceed. This means any number greater than 9.47 is part of the solution. When representing this on a number line, use an open circle to indicate that 9.47 itself is not included in the solution.
Tips
 Incorrectly adding or subtracting numbers. Always doublecheck arithmetic when simplifying inequalities.
 Forgetting to change the inequality symbol when dividing by a negative number. This specific example does not change the inequality since 3.3 is positive, but it's a good habit to remember.
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