which phrases can be used to represent the inequality 12 - 3x≥9? select two options. twelve less than three…

which phrases can be used to represent the inequality 12 - 3x≥9? select two options. twelve less than three times a number is greater than or equal to nine. twelve less than three times a number is at least nine. twelve minus the product of three and a number is greater than or equal to nine. twelve minus the product of three and a number is no more than nine. twelve minus the product of three and a number is no smaller than nine.

which phrases can be used to represent the inequality 12 - 3x≥9? select two options. twelve less than three times a number is greater than or equal to nine. twelve less than three times a number is at least nine. twelve minus the product of three and a number is greater than or equal to nine. twelve minus the product of three and a number is no more than nine. twelve minus the product of three and a number is no smaller than nine.

Answer

Explanation:

Step1: Analyze the inequality components

The expression $12 - 3x$ means twelve minus the product of three and a number $x$. The symbol $\geq$ means "greater than or equal to" or "no smaller than".

Step2: Evaluate each option

  • Option 1: "Twelve less than three times a number" is $3x - 12$, not $12 - 3x$, so it's wrong.
  • Option 2: "Twelve less than three times a number" is $3x - 12$, not $12 - 3x$, so it's wrong.
  • Option 3: "Twelve minus the product of three and a number is greater than or equal to nine" correctly represents $12 - 3x\geq9$.
  • Option 4: "No more than" means $\leq$, so "Twelve minus the product of three and a number is no more than nine" represents $12 - 3x\leq9$, it's wrong.
  • Option 5: "Twelve minus the product of three and a number is no smaller than nine" correctly represents $12 - 3x\geq9$ as "no smaller than" means $\geq$.

Answer:

Twelve minus the product of three and a number is greater than or equal to nine. Twelve minus the product of three and a number is no smaller than nine.