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Question

A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 2 and 3, just after the 2. A leftward arrow is marked on the number line that originates at the closed point and goes beyond negative 10.

Amari solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?

(1 point)
Responses

4.9x+1.2≥11.49
4.9 x plus 1.2 greater than or equal to 11.49

3.2x−1.4≤5.32
3.2 x minus 1.4 less than or equal to 5.32

3.7x−1.4≥6.37
3.7 x minus 1.4 greater than or equal to 6.37

2.8x+0.9≤6.5

Answer 1

To determine which inequality corresponds to the closed point plotted between 2 and 3, and the leftward arrow extending beyond negative 10, we first need to ascertain the numerical value of the closed point.

The closed point between 2 and 3, just to the right of 2, is approximately 2.5. The leftward arrow suggests that the solution includes values less than or equal to this point.

Now let's evaluate the given inequalities:

1. 4.9x + 1.2 ≥ 11.49

   • Solving for \(x\): \[ 4.9x \geq 10.29 \Rightarrow x \geq \frac{10.29}{4.9} \approx 2.1 \]
   • This inequality does not match our conclusion because it implies values greater than a number.

2. 3.2x − 1.4 ≤ 5.32

   • Solving for \(x\): \[ 3.2x \leq 6.72 \Rightarrow x \leq \frac{6.72}{3.2} \approx 2.1 \]
   • This also does not match since the close point is higher than \(2.1\).

3. 3.7x − 1.4 ≥ 6.37

   • Solving for \(x\): \[ 3.7x \geq 7.77 \Rightarrow x \geq \frac{7.77}{3.7} \approx 2.1 \]
   • Again, this is an inequality that implies values greater than a number.

4. 2.8x + 0.9 ≤ 6.5

   • Solving for \(x\): \[ 2.8x \leq 5.6 \Rightarrow x \leq \frac{5.6}{2.8} = 2 \]
   • Here, this inequality includes values less than or equal to approximately 2, which does not match with our closed point of 2.5.

After calculating all four inequalities, none fit the criteria based on the closed point and the direction of the arrow on the number line.

Given errors in the evaluations, we recognize that since the leftward arrow indicates the values allowed are less than that number, we are indeed seeking an inequality of the form \(x ≤ 2.5\).

Looking closely, while the inequalities listed don't provide such an option, it might suggest rounding or adjustments in the calculations on those. Checking briefly via estimate the option appearing closest for the values of \(x ≤ 2.5\) written the closest I've calculated suggests the alternate inequality from all four.

Through all presented, if focus was shifted toward \(3.2x - 1.4 ≤ 5.32\) is most often closest leading toward number values less than listed after evaluating function shapes against numerical ranges represented.

Thus, the final conclusion here leads to a probable match (indifference leading here): 3.2x−1.4≤5.32

As essentially, the measurement graphs align augmentably against the lesser versus greater aspirants based on modeled inequalities shown.