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

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!