Question
10 The product of -4 and a number is greater than 12 . Which solution from the set makes an inequally represented by the statement true?
Ask by Flynn Cox. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The number
satisfies the inequality
.
Solution
To solve the inequality:
-
Isolate
: Divide both sides by. Remember, dividing by a negative number reverses the inequality sign: -
Identify the solutions from the set
that satisfy : -
: Yes, -
: No, is not less than -
: Without additional information about , we cannot determine if -
, , , : No, all these values are greater than
-
-
Conclusion:The only definite solution from the set that satisfies the inequality
is .
Answer:
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Beyond the Answer
To solve the inequality, we start with the expression representing the product of -4 and a number
:
Dividing by -4 (and flipping the inequality sign) gives
.
Now we can look at the solution set
and see which numbers are less than -3. Clearly, -6 is less than -3, making it a valid solution to the inequality.
In contrast, -3 is not less than -3 and the other numbers all exceed this threshold. So, from the set provided, -6 is the only number that makes the inequality true!