Question

Translate the sentence into an inequality.Seven subtracted from the product of 5 and a number is at least -28.Use the variable c for the unknown number.

Answer 1

We have to translate "Seven subtracted from the product of 5 and a number is at least -28".

We start with the product of 5 and a number, which we will call "c":

`5\cdot c`

Seven substracted from the product 5c is equal to:

`5c-7`

This difference is at least -28, meaning that is equal or greater than -28:

`5c-7\ge-28`

We can solve this as:

`\begin{gathered} 5c-7\ge-28 \\ 5c\ge-28+7 \\ 5c\ge-21 \\ c\ge-(21)/(5) \end{gathered}`

Answer: the sentence is represented by 5c - 7 ≥ -28.