Questions: Solve the absolute value inequality. Graph the solution set. x+3+1<3

Solve the absolute value inequality. Graph the solution set. x+3+1<3
Transcript text: Solve the absolute value inequality. Graph the solution set. \[ |x+3|+1<3 \]
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Solution

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Solution Steps

Step 1: Solve the Inequality

The given inequality is:

\[ |x+3|+1<3 \]

First, subtract 1 from both sides:

\[ |x+3| < 2 \]

This inequality can be split into two separate inequalities:

\[ -2 < x+3 < 2 \]

Step 2: Solve the Compound Inequality

Now, solve the compound inequality:

  1. Solve \(-2 < x+3\):

    \[ -2 - 3 < x \implies x > -5 \]

  2. Solve \(x+3 < 2\):

    \[ x < 2 - 3 \implies x < -1 \]

Final Answer

The solution set is:

\[ -5 < x < -1 \]

{"axisType": 3, "coordSystem": {"xmin": -6, "xmax": 0, "ymin": -1, "ymax": 1}, "commands": ["y = 0"], "latex_expressions": ["$-5 < x < -1$"]}

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