Given the sentence: "Nine increased by the product of a number and 6 is greater than or equal to -18", you need to know the following in order to translate it into an inequality:
1. The word "increased" indicates an Addition.
2. A Product is the result of a Multiplication.
3. The inequality symbol whose meaning is "Greater than or equal to" is:
[tex]\ge[/tex]Let be "x" the unknown number.
Then, you can write the following expression to represent the product of a number and 6:
[tex]6x[/tex]Therefore, "Nine increased by the product of a number and 6" is:
[tex]9+6x[/tex]Knowing that this expression is greater than or equal to -18, you can write the following inequality:
[tex]9+6x\ge-18[/tex]Hence, the answer is:
[tex]9+6x\ge-18[/tex]