High School

Indicate the answer choice that best completes the statement or define a variable, write an inequality, and solve each problem.

Negative three times a number is at least 57.

a. [tex](-3n \geq 57; \{n \mid n \leq -19\})[/tex]

b. [tex](-3n \leq 57; \{n \mid n \geq -19\})[/tex]

c. [tex](-3n \geq 57; \{n \mid n \leq 19\})[/tex]

d. [tex](-3n > 57; \{n \mid n < -19\})[/tex]

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]