Question

mr. clarke plans to buy 3 security cameras to install outside his donut shop. he wants to spend less than $450 on the cameras in all. let x represent how much mr. clarke wants to spend on each camera. which inequality describes the problem? 3x < 450 3x ≤ 450 solve the inequality. then, complete the sentence to describe the solution. mr. clarke wants to spend less than $\boxed{}$ on each camera.

Explanation:

Part 1: Choosing the correct inequality

Mr. Clarke is buying 3 cameras, and \( x \) is the cost per camera. The total cost is \( 3x \). He wants to spend less than $450, so the inequality is \( 3x < 450 \) (since "less than" corresponds to the \( < \) symbol, not "less than or equal to").

Step 1: Isolate \( x \)

To solve \( 3x < 450 \), divide both sides by 3.
\( \frac{3x}{3} < \frac{450}{3} \)

Step 2: Simplify

Simplifying both sides gives \( x < 150 \).

Answer:

\( 3x < 450 \)

Part 2: Solving the inequality