Middle School

Negative three times a number is at least 57.

a. \(-3n \geq 57; \{n \leq -19\}\)
b. \(-3n \leq 57, n \geq -19\)
c. \(-3n \geq 57, \{n \leq -19\}\)
d. \(-3n > 57, \{n < -19\}\)

Answer :

The option formatting isn't very clear, anyway: given a number x, negative 3 times that number is -3x. If this has to be at least 57, it means that -3x must be greater than or equal to 57:

[tex]-3x\geq 57[/tex]

Dividing both sides by -3 solves the equation, but we have to switch the inequality sign because we're dividing by a negative number:

[tex]x\leq \dfrac{57}{3}=19[/tex]

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