Question

practice comparing positive and negative numbers
study the example showing how to compare two negative numbers. then solve problems 1–5.
example
the table shows the amount of money savanna either withdraws (–) or deposits (+) into her bank account over 5 weeks. write an inequality to compare the withdrawals for week 2 and week 3.

week	week 1	week 2	week 3	week 4	week 5
amount	+$40	–$40	–$60	+$100	–$80

plot the amounts on a number line.
(number line with week 2 at –60? wait, no, the number line has marks at –80, –60, –40, –20, 0, 20, 40. week 2 is at –40? wait, the example says: –60 is to the left of –40. so –60 < –40.

1. a. compare the two amounts in the example using the symbol ≥.

b. does using > for the inequality change which amount represents withdrawing more money? explain.

1. write an inequality that compares the value of point a and the value of point b. show your work.

(number line with a and b, 0, 5, 10 marked. a is to the left of b, left of 0?)
vocabulary
inequality: a mathematical statement that uses an inequality symbol to show the relationship between values of expressions.

Explanation:

Part 1a

Step1: Identify amounts

Week 2 withdrawal: $-\$40$, Week 3 withdrawal: $-\$60$.

Step2: Recall inequality for negatives

For negative numbers, the one with larger magnitude is smaller. $|-60| = 60$, $|-40| = 40$. Since $60 > 40$, $-60 < -40$ is reversed for $\geq$. Wait, no—wait, the question is to use $\geq$. Wait, original comparison was $-60 < -40$, so in terms of $\geq$, we check: Is $-40 \geq -60$? Yes, because $-40$ is to the right of $-60$ on the number line (greater). So $-40 \geq -60$.

Withdrawing more money means a more negative (or larger magnitude negative) amount. The inequality symbol direction doesn't change the actual amounts' magnitudes. $-60$ (Week 3) has a larger magnitude than $-40$ (Week 2), so Week 3 withdrew more. Using $>$ (e.g., $-40 > -60$) still shows $-40$ is greater, but the withdrawal amounts' magnitudes (who withdrew more) depend on absolute values, not the inequality symbol's direction. So no, it doesn't change which amount is a larger withdrawal.

Step1: Determine positions on number line

Assume the number line has intervals. Let's see the scale: from the diagram, 0, 5, 10. So each tick might be 5 units? Wait, the points A and B: A is to the left of B. Let's assign values. Suppose the leftmost tick is, say, -15, then A is at -10, B at -5? Wait, no—wait, the number line has 0, 5, 10 on the right. So moving left from 0, each tick is -5? Let's check: If B is closer to 0 than A. So A is at a more negative (smaller) value than B. So if A is at, say, -10 and B at -5 (or similar), then A < B.

Step2: Write inequality

Since A is to the left of B on the number line, the value of A is less than the value of B. So if A’s value is $a$ and B’s is $b$, then $a < b$.

Answer:

$-40 \geq -60$

Part 1b