To determine which inequality Bashira solved based on the graph provided, we note the following from your description:
- The open point at \( 6 \frac{2}{3} \) suggests that the solution to the inequality does not include the number \( 6 \frac{2}{3} \), indicating it is likely a greater-than inequality.
- The rightward arrow going beyond 10 further confirms that the solution continues infinitely in the positive direction.
Now let's convert \( 6 \frac{2}{3} \) to an improper fraction: \[ 6 \frac{2}{3} = 6 + \frac{2}{3} = \frac{18}{3} + \frac{2}{3} = \frac{20}{3} \]
This means we are looking for an inequality of the form: \[ x > \frac{20}{3} \]
Now, let's analyze the response options:
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15x > 113
- Dividing both sides by 15: \[ x > \frac{113}{15} \approx 7.53 \] (this is greater than \( 6 \frac{2}{3} \))
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Start Fraction 1 over 5 end fraction x greater than 1 Start Fraction 1 over 3 end fraction
- This translates to: \[ \frac{1}{5} x > \frac{4}{3} \]
- Multiplying both sides by 5: \[ x > \frac{20}{3} \] (matches our target)
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12x > 314
- Dividing both sides by 12: \[ x > \frac{314}{12} \approx 26.17 \] (not applicable)
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14x > 212
- Dividing both sides by 14: \[ x > 15.14 \] (not applicable)
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13x > 225
- Dividing both sides by 13: \[ x > 17.31 \] (not applicable)
The only inequality that corresponds correctly to the open point at \( 6 \frac{2}{3} \) and extends to the right (greater than) is: \[ \frac{1}{5}x > \frac{4}{3} \]
Thus, the correct response is: Start Fraction 1 over 5 end fraction x greater than 1 Start Fraction 1 over 3 end fraction.
1 answer