Question

33 graph the solution to the inequality $-2|x - 5| + 7 > 3$

Explanation:

Step1: Isolate the absolute value term

Subtract 7 from both sides:
$-2|x-5| > 3 - 7$
$-2|x-5| > -4$

Step2: Divide by negative (reverse inequality)

Divide both sides by -2, flip the inequality sign:
$|x-5| < 2$

Step3: Rewrite as compound inequality

For $|A| < b$ ($b>0$), $-b < A < b$:
$-2 < x - 5 < 2$

Step4: Solve for x

Add 5 to all parts:
$-2 + 5 < x < 2 + 5$
$3 < x < 7$

Step5: Graph the solution

This is an open interval between 3 and 7, so use open circles at 3 and 7, with a line connecting them (matches the second top symbol: open circles at both ends, line in between).

Answer:

The solution is $3 < x < 7$, graphed as an open interval on the number line with open circles at 3 and 7, and the segment between them shaded.