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Answer :
Let's solve the problem: Negative three times a number is at least 57.
1. Define the variable and write the inequality:
Let's define the number as [tex]\( n \)[/tex].
The phrase "Negative three times a number" translates to [tex]\( -3n \)[/tex].
"At least 57" means the expression [tex]\( -3n \)[/tex] is greater than or equal to 57.
So, the inequality is:
[tex]\[
-3n \geq 57
\][/tex]
2. Solve the inequality:
To solve for [tex]\( n \)[/tex], we need to isolate the variable. This involves dividing both sides of the inequality by -3. Remember that when you divide or multiply both sides of an inequality by a negative number, you need to flip the inequality sign.
[tex]\[
n \leq \frac{57}{-3}
\][/tex]
[tex]\[
n \leq -19
\][/tex]
3. Solution:
The solution to the inequality is [tex]\( n \leq -19 \)[/tex].
The answer choice that matches this solution is:
a. [tex]\(-3n \geq 57 ; \{n \mid n \leq -19\}\)[/tex]
1. Define the variable and write the inequality:
Let's define the number as [tex]\( n \)[/tex].
The phrase "Negative three times a number" translates to [tex]\( -3n \)[/tex].
"At least 57" means the expression [tex]\( -3n \)[/tex] is greater than or equal to 57.
So, the inequality is:
[tex]\[
-3n \geq 57
\][/tex]
2. Solve the inequality:
To solve for [tex]\( n \)[/tex], we need to isolate the variable. This involves dividing both sides of the inequality by -3. Remember that when you divide or multiply both sides of an inequality by a negative number, you need to flip the inequality sign.
[tex]\[
n \leq \frac{57}{-3}
\][/tex]
[tex]\[
n \leq -19
\][/tex]
3. Solution:
The solution to the inequality is [tex]\( n \leq -19 \)[/tex].
The answer choice that matches this solution is:
a. [tex]\(-3n \geq 57 ; \{n \mid n \leq -19\}\)[/tex]
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