Questions: Solve the inequality. Graph the solutions. -18+2x-6 ≤ -6 Select the correct choice below and fill in any answer boxes in your choice. A. The solution is x= (Type an integer or a simplified fraction.) B. The solution is x ≤ or x ≥ (Type integers or simplified fractions.) The solution is -3^3 ≤ x ≤ 9^3. (Type integers or simplified fractions.) Di. The solution is all real numbers. E. There is no solution.

Solve the inequality. Graph the solutions. -18+2x-6 ≤ -6 Select the correct choice below and fill in any answer boxes in your choice. A. The solution is x= (Type an integer or a simplified fraction.) B. The solution is x ≤ or x ≥ (Type integers or simplified fractions.) The solution is -3^3 ≤ x ≤ 9^3. (Type integers or simplified fractions.) Di. The solution is all real numbers. E. There is no solution.
Transcript text: Solve the inequality. Graph the solutions. \[ -18+|2 x-6| \leq-6 \] Select the correct choice below and fill in any answer boxes in your choice. A. The solution is $x=$ $\square$ (Type an integer or a simplified fraction.) B. The solution is $x \leq$ $\square$ or $x \geq$ $\square$ (Type integers or simplified fractions.) The solution is $-3^{3} \leq x \leq 9^{3}$. (Type integers or simplified fractions.) Di. The solution is all real numbers. E. There is no solution.
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Solution

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Solution Steps

Step 1: Simplify the inequality

Given the inequality: \[ -18 + |2x - 6| \leq -6 \] First, isolate the absolute value term: \[ |2x - 6| \leq -6 + 18 \] \[ |2x - 6| \leq 12 \]

Step 2: Solve the absolute value inequality

The inequality \(|2x - 6| \leq 12\) can be split into two inequalities: \[ -12 \leq 2x - 6 \leq 12 \]

Step 3: Solve for \(x\)

Add 6 to all parts of the inequality: \[ -12 + 6 \leq 2x \leq 12 + 6 \] \[ -6 \leq 2x \leq 18 \] Divide by 2: \[ -3 \leq x \leq 9 \]

Final Answer

The solution is: \[ -3 \leq x \leq 9 \]

{"axisType": 3, "coordSystem": {"xmin": -10, "xmax": 10, "ymin": -2, "ymax": 2}, "commands": ["y = -18 + abs(2*x - 6)", "y = -6"], "latex_expressions": ["$y = -18 + |2x - 6|$", "$y = -6$"]}

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