Questions: Solve the following inequality. Graph the solution set. [ x-9+3<9 ] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There are infinitely many solutions. The solution set is . ... (Type your answer in interval notation.) B. There are finitely many solutions. The solution set is (Use a comma to separate answers as needed.) C. There is no real solution.

Solve the following inequality. Graph the solution set.
[
x-9+3<9
]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. There are infinitely many solutions. The solution set is .
... (Type your answer in interval notation.)
B. There are finitely many solutions. The solution set is
(Use a comma to separate answers as needed.) 
C. There is no real solution.
Transcript text: Solve the following inequality. Graph the solution set. \[ |x-9|+3<9 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There are infinitely many solutions. The solution set is $\square$ . ... (Type your answer in interval notation.) B. There are finitely many solutions. The solution set is (Use a comma to separate answers as needed.) $\square$ C. There is no real solution.
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Solution

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Solution Steps

Step 1: Solve the inequality

Given the inequality: \[ |x-9|+3<9 \]

First, isolate the absolute value term: \[ |x-9| < 6 \]

This inequality can be split into two separate inequalities: \[ -6 < x-9 < 6 \]

Step 2: Solve the inequalities

Solve each part of the compound inequality: \[ -6 < x-9 \quad \text{and} \quad x-9 < 6 \]

Add 9 to all parts of the inequality: \[ -6 + 9 < x < 6 + 9 \] \[ 3 < x < 15 \]

Final Answer

The solution set in interval notation is: \[ (3, 15) \]

Plot Information

{"axisType": 3, "coordSystem": {"xmin": 0, "xmax": 18, "ymin": -1, "ymax": 1}, "commands": ["y = 0"], "latex_expressions": ["$3 < x < 15$"]}

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