name symbols of inequalities: reflection choose 3 questions to answer. - when are negative numbers used and why are they important? - why is it useful for me to know the absolute value of a number? - how do i plot points on the number line? - how do i write inequalities using the and and

Question

name
symbols of inequalities: reflection
choose 3 questions to answer.

when are negative numbers used and why are they important?
why is it useful for me to know the absolute value of a number?
how do i plot points on the number line?
how do i write inequalities using the > and < symbols?
how is the absolute value of a number used to determine its distance on a number line?
how can i use vertical and horizontal number lines to solve problems?
how do i compare and order rational numbers?

symbols of inequalities: reflection
e 3 questions to answer.

when are negative numbers used and why are they important?
why is it useful for me to know the absolute value of a number?
how do i plot points on the number line?
how do i write inequalities using the > and < symbols?
how is the absolute value of a number used to determine its distance on a number line?
how can i use vertical and horizontal number lines to solve problems?
how do i compare and order rational numbers?

Accepted Answer

To answer these reflection questions, we'll select three and provide explanations:

### 1. When are negative numbers used and why are they important?
# Brief Explanations:
Negative numbers represent values less than zero (e.g., debt, temperature below zero, elevation below sea level). They are important for quantifying losses, directions (opposite of positive), and balancing positive quantities (e.g., in accounting, science, or navigation).
# Answer:
Negative numbers are used to represent values less than zero (e.g., debt, sub - zero temperatures, elevation below sea level). They are important for quantifying losses, opposite directions (e.g., - 5m means 5m down), and balancing positive quantities (e.g., in financial accounting or scientific measurements).

### 2. Why is it useful to know the absolute value of a number?
# Brief Explanations:
Absolute value ($|x|$) measures a number’s distance from zero (ignoring sign). It is useful for finding magnitudes (e.g., speed, distance, error), comparing values regardless of direction, and solving equations (e.g., $|x| = 5$ has two solutions: 5 and - 5).
# Answer:
The absolute value of a number (e.g., $| - 3|=3$, $|5| = 5$) represents its distance from zero. It is useful for finding magnitudes (e.g., speed, distance, or error, where direction does not matter), comparing values regardless of sign (e.g., “How far is - 4 from 0?”), and solving equations (e.g., $|x| = 2$ implies $x = 2$ or $x=-2$).

### 3. How do I plot points on the number line?
# Brief Explanations:
1. Draw a horizontal/vertical line with a zero (origin) in the middle.
2. Mark positive numbers to the right (or up) of zero, negative numbers to the left (or down).
3. Locate the number’s value: for $x$, move $|x|$ units from zero (right if $x>0$, left if $x < 0$) and mark the point.
# Answer:
1. Draw a number line with a marked origin (0).
2. Label positive numbers to the right of 0, negative numbers to the left.
3. For a number (e.g., 3, - 2, or $1.5$):
   - If positive (e.g., 3), move 3 units to the right of 0 and mark the point.
   - If negative (e.g., - 2), move 2 units to the left of 0 and mark the point.
   - For a fraction/decimal (e.g., $1.5$), divide the interval between 1 and 2 into 2 equal parts and mark the midpoint.

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QUESTION IMAGE

Question

Explanation:

1. When are negative numbers used and why are they important?

Answer:

2. Why is it useful to know the absolute value of a number?