Which number line correctly represents the solutions of the inequality -1 > 4w?
Understand the Problem
The question asks us to identify which number line correctly represents the solution to the inequality -1 > 4w. We need to solve the inequality for 'w' and then compare the solution to the provided number lines to find the correct visual representation.
Answer
C.
Answer for screen readers
C.
Steps to Solve
- Solve the inequality for $w$
Divide both sides of the inequality $-1 > 4w$ by 4: $$ \frac{-1}{4} > \frac{4w}{4} $$ $$ -\frac{1}{4} > w $$
- Rewrite the inequality
Rewrite the inequality so that $w$ is on the left side: $$ w < -\frac{1}{4} $$ Since $-\frac{1}{4} = -0.25$, we have: $$ w < -0.25 $$
- Interpret the solution
The solution $w < -0.25$ means that $w$ can be any number less than $-0.25$, but not equal to $-0.25$. This is represented on a number line by an open circle at $-0.25$, with the line shaded to the left (towards smaller numbers).
- Match the solution to the given number lines
Looking at the number lines, we need to find one with the following features:
- An open circle at $-0.25$
- A line shaded to the left of $-0.25$
Option C has an open circle at $-0.25$ and goes to the left.
C.
More Information
The solution to the inequality $ -1 > 4w $ is $ w < -0.25 $, and is represented by the number line in option C.
Tips
A common mistake is forgetting to flip the inequality sign when dividing or multiplying by a negative number. However, in this case, we divided by a positive number (4), so there is no change to inequality direction.
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