Questions: Solve and write interval notation for the solution set. Then graph the solution set. -3 ≤ x+5 ≤ 3

Solve and write interval notation for the solution set. Then graph the solution set. -3 ≤ x+5 ≤ 3
Transcript text: Solve and write interval notation for the solution set. Then graph the solution set. \[ -3 \leq x+5 \leq 3 \]
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Solution

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Solution Steps

Step 1: Solve the inequality

The given compound inequality is: \[ -3 \leq x+5 \leq 3 \]

Step 2: Isolate \(x\) in the inequality

Subtract 5 from all parts of the inequality: \[ -3 - 5 \leq x + 5 - 5 \leq 3 - 5 \] \[ -8 \leq x \leq -2 \]

Final Answer

The solution set in interval notation is \([-8, -2]\).

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 0, "ymin": -1, "ymax": 1}, "commands": ["y = 0"], "latex_expressions": ["$x \\in [-8, -2]$"]}

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