To determine which inequality corresponds to the given graph, we should first analyze each option logically to check which inequality could produce the values represented in the graph.
Let's rewrite each inequality in a clearer form:
- \( x + \frac{7}{2} \geq -\frac{11}{2} \)
- \( -\frac{1}{2} x + \frac{5}{2} \geq 4 \)
- \( x + \frac{7}{2} \geq \frac{3}{2} \)
- \( x - \frac{7}{2} \geq \frac{3}{2} \)
We can solve each inequality step-by-step to find out their solutions.
-
\( x + 3.5 \geq -5.5 \)
\( x \geq -5.5 - 3.5 \)
\( x \geq -9 \) -
\( -0.5x + 2.5 \geq 4 \)
\( -0.5x \geq 4 - 2.5 \)
\( -0.5x \geq 1.5 \)
\( x \leq -3 \) (multiply by -1, reversed inequality sign) -
\( x + 3.5 \geq 1.5 \)
\( x \geq 1.5 - 3.5 \)
\( x \geq -2 \) -
\( x - 3.5 \geq 1.5 \)
\( x \geq 1.5 + 3.5 \)
\( x \geq 5 \)
Now, if you compare these solutions:
- \( x \geq -9 \)
- \( x \leq -3 \)
- \( x \geq -2 \)
- \( x \geq 5 \)
Since we do not have the graph representation, I cannot conclusively match the solution set. However, based on the options given and typical patterns formed by these inequalities, the one with a positive lower bound greater than or equal to \( 5 \) (the last one) typically contains far away values.
If you provide the graphical representation of the inequalities or more context, I could provide a more accurate response. However, based on the simplified analysis of the inequalities alone, option 4: \( x - 3.5 \geq 1.5 \) leading to \( x \geq 5 \) appears to be valid in creating a solution set that represents an inequality where values begin at an interval greater than or equal to \( 5 \).