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
Find the absolute value inequality representation for:
\( |x + 3| \leq 5 \)
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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