Solve: |-9 + |d + 7| + |-3d - 2|| < 0 - Complex Absolute Value Inequality

Given:

$|-9 + |d + 7| + |-3d - 2|| < 0$

Which of the following statements is necessarily true?

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Given:

$|-9 + |d + 7| + |-3d - 2|| < 0$

Which of the following statements is necessarily true?

The given inequality is: $|-9 + |d + 7| + |-3d - 2| < 0$ .

Both expressions, $|d + 7| \ge 0$ and $|-3d - 2| \ge 0$ , because absolute values cannot be negative.

Adding these with -9, the expression $-9 + |d + 7| + |-3d - 2|$ will be greater than or equal to -9.

Since -9 is not less than 0, the inequality $< 0$ cannot hold true.

Therefore, the statement "No solution" is the correct answer.

No solution

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Given:

$\left|2x-1\right|>-10$

Which of the following statements is necessarily true?

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