Given:
Which of the following statements is necessarily true?
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Given:
Which of the following statements is necessarily true?
To solve the inequality , we rewrite it as two separate inequalities:
Let's solve each one:
For the first inequality :
Add 10 to both sides:
Divide both sides by 5:
For the second inequality :
Add 10 to both sides:
Divide both sides by 5:
Combining these solutions, we have:
or
Therefore, the correct statement regarding the solution set is: or .
or
Given:
\( \left|2x-1\right|>-10 \)
Which of the following statements is necessarily true?
Because absolute value measures distance from zero! If , then 5x - 10 could be either greater than 15 OR less than -15. Both make the distance greater than 15.
For greater than (>), use OR because you want values far from zero on either side. For less than (<), you'd use AND because you want values close to zero.
Remember: means the expression is either very positive (> number) or very negative (< -number). Think of it as "far from zero."
Substitute: . Since 10 is NOT greater than 15, x = 0 should NOT be in your solution set. This confirms or is correct!
Because a single x-value can't be both greater than 5 AND less than -1 at the same time! The solution includes values that satisfy either condition - that's why we use OR.
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