The correct answers are:
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[C]: " 8 " . AND :
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[D]: " 9 " .
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Explanation:
To solve:
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Given: " 2r ≤ 3r − 8 " ;
Simplify; to solve this "inequality" in terms of "r" ;
Subtract "3r" from EACH SIDE of the equation:
→ 2r − 3r ≤ 3r − 8 − 3r ;
to get:
→ - 1r ≤ -8 ;
Now, divide both sides of this "inequality" by "-1" ;
to isolate "r" on one side of the "inequality" ; and to solve; 'in terms of "r" ;
Note: When you multiply or divide each side of an inequality;
→ by a "negative value" ; you ALWAYS reverse the "sign" of the inequality (switch the direction of the "sign").
So:
→ - 1r ≤ -8 ;
Divide each side by: " -1 " ;
to get:
→ - 1r / -1 ≤ -8 / -1 ;
to get:
→ {remember to reverse the direction of the sign} ;
→ " r ≥ 8 " .
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So: given the answer choices: " 6, 7 , 8 , and 9" ;
→ Which of these numbers, if any, when substituted for "r" in the "inequality" ; hold true?
→ Begin; with: " r = 6 " ; → " 6 ≥ 8 " ? ; No.
→ Continue; with: " r = 7 " ; → " 7 ≥ 8 " ? ; No.
→ Continue; with: " r = 8 " ; → " 8 ≥ 8 " ? ; Yes!
→ {Note: Is "8" greater than; OR equal to; "8" ?
→ " 8 = 8 " ; → so; " 8 " is equal to " 8 " !
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→ Continue; with: " r = 9 " ; → " 9 ≥ 8 " ? ; Yes!
→ {Note: Is " 9 " greater than; OR equal to; " 8 " ?
→ " 9 > 8 " ; → so; "9" is greater than " 8 " !
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→ As such: the correct answers are:
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[C]: " 8 " . AND :
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[D]: " 9 " .
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Hope this helps!
Best wishes in your academic endeavors —
and within the "Brainly" community!
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