To solve the inequality \( \frac{5}{6} x < -10 \), we need to isolate \( x \).
To do this, we can multiply both sides of the inequality by the reciprocal of \( \frac{5}{6} \) which is \( \frac{6}{5} \). Since \( \frac{6}{5} \) is positive, the direction of the inequality will stay the same.
Let's solve it step-by-step:
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Start with the original inequality: \[ \frac{5}{6} x < -10 \]
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Multiply both sides by \( \frac{6}{5} \): \[ x < -10 \times \frac{6}{5} \]
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Now calculate the right-hand side: \[ -10 \times \frac{6}{5} = -12 \]
So the final solution to the inequality is: \[ x < -12 \]
Now, analyzing the statements of Juana, Anish, and Giselle:
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Juana: Says the inequality symbol must be reversed because there’s a negative sign in the inequality. This statement is incorrect because we only reverse the inequality symbol when we multiply or divide by a negative number, which is not the case here.
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Anish: Refers to the multiplication property of inequality (which is correct), but we must remember that the symbol does not change when multiplying by a positive number, which is applicable here as we multiplied by \( \frac{6}{5} \).
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Giselle: Says the inequality symbol must stay the same. This statement is correct because we indeed did not multiply or divide by a negative number.
Thus, the correct combination of people is Anish and Giselle, as they are both right in their reasoning about how to handle the inequality (with some clarification needed for Anish about the direction of the symbol). Juana's reasoning is incorrect in this context.
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