Question

3 the typical level of a low tide at a beach is the 0 point on a number line. each day’s high and low tides are measured relative to the typical low tide. on monday morning, low tide is at -0.8 ft. on tuesday morning, low tide is at -0.4 ft.
a. write an inequality to compare the low tides on monday and tuesday mornings. show your work.
solution
b. which day has a higher low tide? explain.
4 consider the inequality $-3 < -2\frac{1}{2}$. what does the inequality tell you about the location of -3 compared to the location of $-2\frac{1}{2}$ on a horizontal number line? use to the right and to the left in your answer.
5 in golf, the winner is the person with the lowest score. at the end of a round of golf, jada’s score is positive. isabel’s score is negative. can you determine who wins? if so, tell who wins and why. if not, explain why not.

Explanation:

Part a

Step1: Identify the values

Monday's low tide: $-0.8$ ft, Tuesday's low tide: $-0.4$ ft.

Step2: Compare the values

On the number line, $-0.8$ is to the left of $-0.4$, so $-0.8 < -0.4$.

Step1: Recall the inequality

From part (a), we have $-0.8 < -0.4$.

Step2: Interpret the inequality

In terms of tide levels, a higher number (closer to 0 or positive) means a higher tide. Since $-0.4 > -0.8$, Tuesday's low tide is higher.

Step1: Recall number line order

On a horizontal number line, smaller numbers (more negative) are to the left, and larger numbers are to the right.

Step2: Analyze the inequality

The inequality is $-3 < -2\frac{1}{2}$. This means $-3$ is less than $-2\frac{1}{2}$.

Step3: Relate to number line position

Since $-3$ is less than $-2\frac{1}{2}$, $-3$ is to the left of $-2\frac{1}{2}$ on the horizontal number line.

Answer:

The inequality is $-0.8 < -0.4$.

Part b