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Solve \( -3|x+1| \geq 21 \) A. \( x \geq 6 \) and \( x \geq-8 \) B. \( x \geq-7 \) and \( x \geq 7 \) C. \( x \geq-6 \) and \( x \geq 8 \) D. no solution

Ask by Hart Lyons. in the United States
Mar 12,2025

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Answer

There is no solution.

Solution

Solve the equation \( -3|x+1| \geq 21 \). Solve the inequality by following steps: - step0: Solve for \(x\): \(-3\left|x+1\right|\geq 21\) - step1: The statement is false for any value of \(x:\) \(x \notin \mathbb{R}\) The solution to the inequality \( -3|x+1| \geq 21 \) is that there is no real solution. Therefore, the correct answer is D. no solution.

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To solve the inequality \( -3|x+1| \geq 21 \), we first divide both sides by -3. Remember that dividing or multiplying by a negative number reverses the inequality sign: \[ |x+1| \leq -7 \] The absolute value \( |x+1| \) represents a distance, which cannot be negative. As \( |x+1| \) must always be \( \geq 0 \), this inequality \( |x+1| \leq -7 \) has no solution. Therefore, the answer is: D. no solution The solution is confirmed once we realize that an absolute value cannot be less than a negative number, thereby reinforcing the notion that there's no possible x that satisfies this inequality. For further exploration, think of the properties of absolute values: they always yield non-negative results. If you're curious about equations and inequalities involving absolute values, consider researching their graphical interpretations, as they often manifest as V-shaped graphs with vertices representing solutions!

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