Given:
Which of the following statements is necessarily true?
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Given:
Which of the following statements is necessarily true?
To solve , consider both cases: and .
1. Solving :
Subtract 3 from both sides:
Divide both sides by 5:
2. Solving :
Subtract 3 from both sides:
Divide both sides by 5:
Combining both results, we find .
Given:
\( \left|2x-1\right|>-10 \)
Which of the following statements is necessarily true?
The absolute value |5x + 3| represents distance from zero. For this distance to be ≤ 7, the expression inside must be between -7 and +7, giving you both boundary conditions.
With ≥, you'd use 'or' to combine solutions because you want values outside the interval. With ≤, you use 'and' because you want values inside the interval.
No! You can't just delete the bars. The absolute value creates two cases that must both be satisfied simultaneously for ≤ inequalities.
That's perfectly normal! Convert fractions to decimals for easier comparison: . Your final answer can use either form.
Substitute: . Since 3 ≤ 7 is true, x = 0 is indeed in our solution interval [-2, 0.8].
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