Given:
Which of the following statements is necessarily true?
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Given:
Which of the following statements is necessarily true?
To solve this problem, we start by analyzing the inequality:
According to the properties of absolute values, is always non-negative, so it can only add to 5 or keep it positive.
Therefore, the only value this expression can assume is non-negative. Hence, it can never be less than zero.
Consequently, the original condition is impossible.
The correct answer is that the inequality has no solution.
No solution
No solution
Given:
\( \left|2x-1\right|>-10 \)
Which of the following statements is necessarily true?
Absolute values represent distance from zero, which is always positive or zero. Think of it as asking 'how far?' - you can't be a negative distance away!
Work from the inside out! First calculate |5-1| = 4, then |4+3-4| = |3| = 3. Take it step by step and don't rush.
It means no value of the variable can make the inequality true. The mathematical statement is impossible, like saying 'find a number where 7 < 0'.
Always double-check your arithmetic! But if you correctly get , then 'no solution' is definitely right.
Equations like |a| + 5 = 0 would give a specific answer (though still impossible here). But inequalities like |a| + 5 < 0 ask for a range of values, which doesn't exist.
Write 'No solution' or use the symbol ∅ (empty set). Don't leave it blank or write 'impossible' - be mathematically precise!
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