To determine which inequality Willow solved, we can analyze the expressions given and find the correct solution.
Let's rewrite the inequalities:
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x + 2 1/2 < 2 1/2 can be rewritten as: \[ x + \frac{5}{2} < \frac{5}{2} \] By subtracting \(\frac{5}{2}\) from both sides, we have: \[ x < 0 \]
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x - 2 1/3 < 2 1/6 can be rewritten as: \[ x - \frac{7}{3} < \frac{13}{6} \] To solve for \(x\), we first convert \(\frac{13}{6}\) to a compatible fraction. \(\frac{13}{6}\) can be rewritten as \(\frac{13}{6} = \frac{13 \times 2}{6 \times 2} = \frac{26}{12}\), and \(\frac{7}{3} = \frac{14}{6}\): \[ x < \frac{13}{6} + \frac{7}{3} \] Finding a common denominator (which is 6) gives us: \[ x < \frac{13}{6} + \frac{14}{6} = \frac{27}{6} = 4.5 \] Thus, this inequality simplifies to: \[ x < 4.5 \]
In conclusion, we have determined the solutions of the inequalities:
- \(x < 0\)
- \(x < 4.5\)
Without seeing the graph that Willow produced, we can know that the appropriate representation of a solution to an inequality would show a range of values. If her graph indicated values less than 0, her solution would relate to the first inequality. If it indicated values less than 4.5, it would relate to the second inequality.
If you could provide information on what the number line looks like, we could conclusively determine which inequality was solved. However, as it stands, the likely candidates for these inequalities from Willow's determination are:
- \(x < 0\) from the first inequality.
- \(x < 4.5\) from the second inequality.
So, if you intend to choose between those two inequalities based on the graph representation, it will largely depend on whether it stops at 0 or at 4.5.
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