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

Question

Given:

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

Which of the following statements is necessarily true?

Step-by-Step Solution

The given inequality is: 9+d+7+3d2<0 |-9 + |d + 7| + |-3d - 2| < 0 .

Both expressions, d+70|d + 7| \ge 0 and 3d20|-3d - 2| \ge 0, because absolute values cannot be negative.

Adding these with -9, the expression 9+d+7+3d2-9 + |d + 7| + |-3d - 2| will be greater than or equal to -9.

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

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

Answer

No solution