Inequalities
Isolate the variable for: 3x≤15 and represent this inequality on a number line.
x≤5
What is the opposite of the opposite of -5?
-5
In which quadrant is the point (3,2)?
Quadrant I
A submarine is 100 feet below sea level. What is the absolute value of its position?
| -100ft|
OR
100ft
Simplify the inequality (isolate the variable):
4x−3 ≥ 9
Answer: x≥3
Arrange from least to greatest: 0,−8,3,−2,5
−8,−2,0,3,5
Which point is located in Quadrant III:
A) (2, -4)
B) (-2, -4)
C) (-3, 3)
B) (−2,−4)
Which of the following numbers in the set {3,4,5,6} are possible solutions to the inequality:
2x+3>11
5 and 6 are possible solutions to the inequality.
Translate to an inequality: “A number decreased by 7 is less than 20.”
x−7<20
A scuba diver is 15 ft below sea level. He rises 9 ft. What is his new depth? Show your answer using a number line.
−15+9=−6 ft
His new depth is -6ft OR 6ft below sea level.
What is the distance between the points (4,1) and (4,−2)?
3 units
A student has a balance of -$4 in a lunch account. What does the absolute value of -4 represent in this situation?
$4 owed
OR
The student owes $4.
Simplify the inequality (Isolate the variable):
3(x+2)<18
Answer: x<4
A hiker is 300 ft above sea level. She descends 450 ft. What is her new elevation?
-150ft
The point A(3,2) is reflected across the y-axis.
What are the coordinates of the reflected point and which quadrant would the reflection be in?
(−3,2) in Quadrant II
A town is at an elevation of -150 ft, and a mountain is at +250 ft. What is the TOTAL distance from the town to the mountain?
400 ft
A student needs at least 70 points to pass a test. They already have 45. Write an inequality to find how many more points, x, they need.
Inequality:
45+x ≥ 70
The temperature at 6:00 AM was −3∘F.
By noon, it increased by 7 degrees.
Then the temperature dropped by 12 degrees in the afternoon.
Finally, it rose by 5 more degrees in the evening.
What was the final temperature at the end of the day? Use a number line to show your work.
Start: −3
→ −3+7=4
→ 4−12=−8
→ −8+5=−3
Final Temperature: −3∘F
Point B(−4,5) is reflected across the x-axis, and then the new point is reflected across the y-axis.
What are the coordinates of the final point?
(4,−5)
Two friends are comparing their positions on a number line.
Mia is standing at position −7.
Jordan is standing at position 4.
Who is farther from zero, and how do you know?
Answer:
Mia's distance from 0: ∣ −7 ∣
Jordan's distance from 0: ∣ 4 ∣
Mia is farther from zero because 7 > 4.
Final Answer:
Mia is farther from zero.