Inequalities
What inequality would you use to compare these numbers?
7 _____ -3
7 > -3
When reading the four quadrants on a coordinate plane, in what direction do we move—clockwise or counterclockwise—starting from Quadrant I?
Counterclockwise
Are points (2, 3) and (2, 7) on the same quadrant or different quadrants? How do you know?
same because both points have a positive x and y value
What is the opposite of -20?
20
What is absolute value?
Absolute value is the distance a number is from zero on a number line and distance is always positive!
Solve the inequality:
7+ x < 53
x<46
In which quadrant is the point (-3, 4)?
Quadrant II
What is the distance between the points (–5, 2) and (3, 2)?
8 units
What is the opposite of -2/3? Where is the opposite located on the number line?
The opposite is 2/3. To the right of zero.
What is the absolute value of -20?
The absolute value is 20.
If x≥4, which way do you draw the arrow on the number line, and do you use an open or closed circle?
------->; closed circle
What are the signs of the x and y values in Quadrant IV?
(+, -)
If point A is at (-4, –3) and B is the reflection across the x-axis, what are the coordinates of point B?
Point B is located at (-4,3)
A submarine dives to 300 feet below sea level. What number represents this situation?
-300
Luis says that the |-7| is less than the absolute value of |5|. Do you agree or disagree? Explain.
Disagree because the absolute value of -7 is 7 and the absolute value of 5 is 5. 7 is not less than 5 — it’s greater.
|-7| > |5|
Bob writes the following inequality.
m - 25 > 89
Which values are solutions to the inequality?
a. 130
b. 100
c. 75
d. 135
A & D
True or False: The point (–3, 0) is located in quadrant II. If false, how would you revise this statement?
False.
The point (–3, 0) is located on the x-axis.
Reflect the point (3, 0) across the y-axis. What is the new point?
(-3,0)
Order these numbers from least to greatest.
-80, -50, -64, -90, -35, -51
–90, –80, –64, –51, –50, –35
The number farthest from zero is the smallest!
Order these numbers from least to greatest.
|–3|, -4, |19|, 0, 15
–4, 0, |–3|, 15, |19|
Emma is going to an amusement park. The entry fee is $12, and each ride ticket costs $3. She has $30 to spend. She writes the inequality 12+3r≤30, where r is the number of ride tickets she can buy.
Which values from the set {5, 6, 7, 8} are solutions to the inequality? What does the solution mean in the context of the problem?
Solutions: 5 and 6
This means that Emma can buy 5 or 6 ride tickets without spending more than $30.
Points A(4, 2), B(4, –5), and C(–3, –5) are three vertices of rectangle ABCD.
What is the order pair of point D?
Point D: (–3, 2)
Evan walks from his house to the park along the path shown on a coordinate grid. His house is at (2, 3) and the park is at (2, 8), then he walks from the park to the library at (6, 8). Distances on the coordinate plane are measured in city blocks.
How many city blocks does Evan walk in total from his house to the library?
9 city blocks
The following cities had these lowest temperatures recorded last winter:
Denver: –5°F
Anchorage: –22°F
Miami: 32°F
New York: –8°F
Chicago had a low temperatute of –12°F. Which city or cities above had a lower temperature than Chicago?
Anchorage
Sofia is thinking of a number. She gives 3 clues:
The number is less than zero.
Its absolute value is between 3 and 6.
The number is even.
What number is Sofia thinking of?
-4