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