To determine which inequality represents the graph, we need to analyze the inequality statements provided. Each of these inequalities can be solved for \(x\) to find the solution set that would correspond to a line on a graph. Here's how to solve each one:
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\(3x - 7 \leq -10\): \[ 3x \leq -10 + 7 \ 3x \leq -3 \ x \leq -1 \]
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\(-3x + 7 < 10\): \[ -3x < 10 - 7 \ -3x < 3 \ x > -1 \quad (\text{flipping the inequality sign when dividing by a negative number}) \]
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\(3x + 7 > 10\): \[ 3x > 10 - 7 \ 3x > 3 \ x > 1 \]
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\(-3x - 7 \geq -10\): \[ -3x \geq -10 + 7 \ -3x \geq -3 \ x \leq 1 \quad (\text{flipping the inequality sign when dividing by a negative number}) \]
Next, we can summarize the solution sets:
- \(3x - 7 \leq -10\) represents all \(x\) values less than or equal to \(-1\).
- \(-3x + 7 < 10\) represents all \(x\) values greater than \(-1\).
- \(3x + 7 > 10\) represents all \(x\) values greater than \(1\).
- \(-3x - 7 \geq -10\) represents all \(x\) values less than or equal to \(1\).
Based on the direction of the inequalities and the ranges they cover, you can identify which inequality corresponds to the graph. If you can provide additional information about the type of graph (e.g., solid or open circles, the direction of shading, etc.), I can help you determine the correct inequality. If the focus is on whether the endpoint is included (closed circle) or not (open circle), please confirm that as well!
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