To determine which inequality Amari solved, we can analyze the positioning of the closed point on the number line. The point is located between 2 and 3, suggesting it represents a value that is greater than or equal to 2 but less than or equal to 3.
Let's convert the possible inequalities into their solutions to see which one aligns with the position of the closed point:
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For the first inequality: \(2.8x + 0.9 \leq 6.5\)
Subtract 0.9 from both sides: \[ 2.8x \leq 5.6 \] Divide by 2.8: \[ x \leq 2 \] (This doesn't match the point which is greater than 2.)
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For the second inequality: \(4.9x + 1.2 \geq 11.49\)
Subtract 1.2 from both sides: \[ 4.9x \geq 10.29 \] Divide by 4.9: \[ x \geq 2.1 \] (This also doesn't match because we need a closed interval at the point.)
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For the third inequality: \(3.7x - 1.4 \geq 6.37\)
Add 1.4 to both sides: \[ 3.7x \geq 7.77 \] Divide by 3.7: \[ x \geq 2.1 \] (This gives a value greater than the closed point.)
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For the fourth inequality: \(3.2x - 1.4 \leq 5.32\)
Add 1.4 to both sides: \[ 3.2x \leq 6.72 \] Divide by 3.2: \[ x \leq 2.1 \] This implies \( x \) could take values less than or equal to approximately 2.1, which includes values from 2 up to 2.1.
Since the closed point is greater than 2 and extends leftward (since it's closed, it includes 2.1), Amari likely solved the fourth inequality, \(3.2x - 1.4 \leq 5.32\). Thus, that matches well with the closed point being plotted just over 2.
Therefore, the correct response is: 3.2x−1.4≤5.32.