Given:
Which of the following statements is necessarily true?
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Given:
Which of the following statements is necessarily true?
The given inequality is: .
This translates to checking if the sum of absolute values and other constants can yield a negative result.
Let's consider the expression inside the absolute values:
for all real numbers .
The absolute value of any expression is always non-negative. Therefore, and .
Adding these non-negative values to -5 will still yield a result that is greater than or equal to -5. Since -5 is not less than 0, the inequality cannot hold true for any real number .
Hence, the statement "No solution" is correct.
No solution
Given:
\( \left|2x-1\right|>-10 \)
Which of the following statements is necessarily true?
By definition, absolute value measures distance, and distance is never negative. So for any real number x.
It doesn't matter! Even if equals -10, the absolute value of -10 is still +10, which is positive.
Look for patterns like |expression| < 0. Since absolute values are never negative, these inequalities are always impossible.
No! The minimum value of is 0, which occurs when the inside expression equals 0. Since 0 is not less than 0, no value of b works.
No solution means the inequality is never true. All real numbers means it's always true. This problem has no solution because absolute values can't be negative.
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