Question

lesson 24 session 2
name
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 -80, -60, -40, 20, 0, 20, 40. week 2 is at -40? wait, the text 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.
2 write an inequality that compares the value of point a and the value of
point b. show your work.
(number line for problem 2: a and b are on the left side of 0, a is to the left of b.)
vocabulary
inequality
a mathematical
statement that
uses an inequality
symbol to show the
relationship between
values of expressions.
solution
lesson 24 compare positive and negative numbers $63

Explanation:

Step1: Analyze the number line for points A and B

Looking at the number line, we can see the positions of point A and point B. Let's assume the scale: each tick mark represents a certain value. From the number line, point A is to the left of point B. In a number line, numbers to the left are smaller than numbers to the right. Let's determine the values. Let's say the distance from 0 to the first tick left of 0: let's assume the ticks are in intervals. Let's see, the number line has 0, 5, 10 on the right. So to the left, the ticks would be negative. Let's find the values of A and B. Let's say the tick marks are spaced by 5 units? Wait, no, looking at the number line, the points A and B are on the left side of 0. Let's count the ticks. From 0, moving left: first tick left of 0 is -5? Wait, no, the number line shows A and B to the left of 0. Let's see the positions: A is two ticks left of 0? Wait, no, the number line has A and B, then 0, 5, 10. Let's assume each tick is 5 units. So point A: let's say the first tick left of 0 is -5, then next is -10? Wait, no, maybe each tick is 5. Wait, the number line has A, then a tick, then B, then a tick, then 0. Wait, maybe the scale is 5 units per tick. So point A is at -10, point B is at -5? Wait, no, let's look again. The number line: A is on the left, B is to the right of A, then 0. So if we consider the direction, numbers to the left are smaller. So if A is at a position left of B, then A < B. Wait, but let's check the coordinates. Let's assume the number line: the first tick left of 0 is -5, then -10? No, maybe the ticks are 5 units. Wait, the problem says "Write an inequality that compares the value of point A and the value of point B". So on the number line, as we move to the right, numbers increase. So point A is to the left of point B, so the value of A is less than the value of B. So if A is at, say, -10 and B is at -5, then -10 < -5. Wait, but let's see the number line: A is two ticks left of 0? Wait, no, the number line has A, then a tick, then B, then a tick, then 0. So from 0, moving left: first tick is -5, then -10? No, maybe each tick is 5. So A is at -10, B is at -5. So A < B. Wait, but let's confirm. The number line: A is to the left of B, so A's value is less than B's value. So the inequality is A < B, or if we denote their values as, say, \( a \) for A and \( b \) for B, then \( a < b \). Wait, but let's check the positions. Let's say the number line has A at -10, B at -5 (since each tick is 5 units: 0, 5, 10 on the right; -5, -10 on the left). So A is at -10, B is at -5. Then -10 < -5, so \( A < B \) (if A is -10 and B is -5) or \( B > A \). Wait, but the problem is to compare point A and point B. So we need to find their values. Let's assume the number line: the distance between 0 and 5 is 5, so each tick is 5 units. So moving left from 0: first tick is -5, second is -10. So point A is at -10, point B is at -5. So the value of A is -10, value of B is -5. So -10 < -5, so \( A < B \) (or \( -10 < -5 \)). Wait, but maybe the ticks are 5 units. So A is at -10, B is at -5. So the inequality is \( A < B \) (or \( -10 < -5 \)).

Step2: Write the inequality

Since point A is to the left of point B on the number line, and on a number line, numbers increase as we move to the right, the value of point A is less than the value of point B. So if we let \( a \) be the value of point A and \( b \) be the value of point B, then \( a < b \). Alternatively, if we can determine the exact values, from the number line, assuming each tick is 5 units, point A is at -10 and point B is at -5, so \( -10 < -5 \), which can be written as \( A < B \) (if A is -10 and B is -5) or specifically, if we take their coordinates, say A is -10 and B is -5, then \( -10 < -5 \).

Answer:

The inequality comparing point A and point B is \( A < B \) (or if their values are -10 and -5, then \( -10 < -5 \)).