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Which inequality represents the graph below:

l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l
0 1
<----------------------------;
(1 point)
Responses

−3x+7<10
−3x+7<10

−3x−7≥−10
negative 3 x minus 7 is greater than or equal to negative 10

3x−7≤−10
3 x minus 7 is less than or equal to negative 10

3x+7>10

1 answer

To determine which inequality represents the given graph, we need to analyze the options in relation to the information provided:

  1. The graph shows a horizontal line with arrows indicating that it is continuing indefinitely to the left. This suggests that the solution involves a range of \(x\) values on one side of a boundary.

  2. The key will be in identifying the type of inequality that corresponds to the boundary.

Let's analyze the options:

  1. −3x + 7 < 10

    • To solve for \(x\): \(-3x < 3\) \ \(x > -1\)
    • This inequality represents values greater than \(-1\), which does not match the graph.

  2. −3x − 7 ≥ −10

    • To solve for \(x\): \(-3x ≥ -3\) \ \(x ≤ 1\)
    • This indicates \(x\) values less than or equal to \(1\), which could fit the graph but depends on the direction of the shading.

  3. 3x − 7 ≤ −10

    • To solve for \(x\): \(3x ≤ -3\) \ \(x ≤ -1\)
    • This indicates values less than or equal to \(-1\), which does not match the graph.

  4. 3x + 7 > 10

    • To solve for \(x\): \(3x > 3\) \ \(x > 1\)
    • This would imply \(x\) values greater than \(1\), which does not fit the graph.

Based on the analysis, the only inequality that potentially fits is −3x − 7 ≥ −10, which translates to \(x ≤ 1\). Thus, the graph would have its critical point at \(1\) (with shading extending leftward, inclusive of \(1\)).

Therefore, the correct inequality that represents the graph is:

−3x−7≥−10.