Question

two thirds of the employees at an office stated that they preferred soft cookies over crispy cookies. more than 36 employees stated their preference. ren was asked to write, solve, and graph an inequality to find the number of employees working at the office. his work is shown below. step rens work step 1 \\(\frac{2}{3}x < 36\\) step 2 \\(x < 54\\) step 3 (number line with 51, 52, 53, 54 (open circle), 55, 56, 57, arrow left from 54) where, if any, did ren first make a mistake in his work?

Explanation:

Step1: Analyze the inequality setup

The problem states "more than 36 employees" preferred soft cookies. Let \( x \) be the number of employees. Two - thirds of the employees is \( \frac{2}{3}x \). Since more than 36 employees preferred soft cookies, the correct inequality should be \( \frac{2}{3}x>36 \), not \( \frac{2}{3}x < 36 \). So Ren made a mistake in Step 1.

Step2: Check subsequent steps (optional for identifying first mistake)

Even though we can check Step 2 and Step 3, since the first mistake is in the setup of the inequality in Step 1, we can conclude the first mistake is in Step 1.

Answer:

Step 1