Question

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

Answer 1

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**.