Question

solve the inequality. then graph the solution set. |x - 2| < 7
choose the correct graph below.
a.
b.
c.
d.
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Explanation:

Step1: Remove absolute - value

If \(|a|\lt b\) (\(b > 0\)), then \(-b\lt a\lt b\). Here \(a=x - 2\) and \(b = 7\), so \(-7\lt x - 2\lt7\).

Step2: Solve the compound - inequality

Add 2 to all parts of the compound - inequality: \(-7+2\lt x-2 + 2\lt7 + 2\), which simplifies to \(-5\lt x\lt9\).

Answer:

The solution set is \(-5\lt x\lt9\). The correct graph is a number line with an open circle at \(-5\) and an open circle at \(9\) and the line segment between them shaded. Without seeing the exact details of the graphs A, B, C, D in a more precise way, if we assume the standard representation of open - ended intervals on a number line, the correct graph should be the one that shows an open circle at \(-5\), an open circle at \(9\), and the line between them shaded.