Question

Translate the sentence into an inequality.

Nine subtracted from the product of 6 and a number is at most -16
Use the variable b for the unknown number.

Answer 1

`6\,b-9\leq -16`

Explanation:

SInce the sentence reads "Nine subtracted from..." start by creating the quantity that 9 would be subtracted from, to make the expression more obvious. So let's begin by making the product of 6 times a "number" (unknown value) and use for the unknown the letter "b" as requested:

`6\,b`. Now proceed to subtract 9 from this expression:

`6\,b-9`

The sentence now continues saying that this expression is at most -16. So we understand that the quantity we created above has to be smaller or at most equal to -16. Therefore, we use the inequality symbol "
`\leq`" to complete the sentence in mathematical terms:

`6\,b-9\leq -16`