Question

Translate thefollowing phaseinto an inequality-3 times r is at least 33A) inequality B) Solve the equality for r.C) express the solution in interval notation.

Answer 1

Given the phrase:

-3 times r is at least 33

Let's translate the given phrase into an inequality.

• Part A.

Let's figure out the inequality in steps.

-3 times r is written as:

-3r

-3 times s is at least 33 means that -3r is greater than or equal to 33.

Hence, we have the inequality:

`-3r\ge33`

• Part B.

Let's solve the inequality for r.

To solve for r, divide both sides of the inequality by -3:

`\begin{gathered} (-3r)/(-3)\ge(33)/(-3) \\ \\ r\le-11 \end{gathered}`

• Part C.

Let's express the solution in interval notation.

Here, the solution is:

`r\le-11`

It means s must be less than or equal to 11.

Therefore, the solution in interval notation is:

`(-\infty,-11\rbrack`

ANSWER:

• A) -3r ≥ 33

• B) r ≤ -11

• C) (-∞, -11]