Question

|2x - 3|>7
select the correct graph for the solution for this inequality.
then choose all possible solutions.
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□ x = - 3
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Explanation:

Step1: Solve the absolute - value inequality

For \(|2x - 3|>7\), we consider two cases:
Case 1: \(2x - 3>7\)
Add 3 to both sides: \(2x-3 + 3>7 + 3\), so \(2x>10\). Divide both sides by 2: \(x > 5\).
Case 2: \(2x - 3<-7\)
Add 3 to both sides: \(2x-3 + 3<-7 + 3\), so \(2x<-4\). Divide both sides by 2: \(x<-2\).

Step2: Analyze the solution on the number - line

The solution set of the inequality \(|2x - 3|>7\) is \(x<-2\) or \(x > 5\). On the number - line, this is represented by an open circle at \(x=-2\) and shading to the left, and an open circle at \(x = 5\) and shading to the right.

Answer:

The graph with an open circle at \(x=-2\) and shading to the left and an open circle at \(x = 5\) and shading to the right; \(x=-3\) is a possible solution since \(-3<-2\).