Vocab
How can we represent a solution set?
Curly Brackets { }
Based off this solution, what kind of problem is this?
3<x<8 where written in set notation { x | 3<x<8 }
AND
How can this be written:
Open circle at 3, shading to the right.
x>3
Write an inequality that represents this problem.
A machine weighs bags of flour. The weight filled bag of flour should be no more than 0.05 pounds from the target weight of 7 pounds. Let w represent the amount of weight.
|w-7| ≤ 0.05
What does AND usually look like on a number line?
It's between two solutions. It would be shaded in between them.
Based off this solution, what kind of problem is this?
x≤−2 OR x>4
where written in set notation { x | x≤−2 or x>4 }
OR
How can this be written:
Closed circle at −2, shading to the left.
x ≤ −2
Write an inequality that represents this problem.
A team uses volleyballs that have certain weights for games. Each volleyball must not be more than 10 grams from the desired weight of 270 grams. Let w represent the weight of each volleyball in grams.
|w-270| ≤ 10
What does OR usually look like on a number line?
The solutions go in different directions. (left and right depending on where the inequality signis facing)
Solve −19 < |5x+1| < 14
−4 < x < 13/5, −4 < x < 2.6, x< 2.6 AND x > −4
How can this be written:
Open circle at −4 and open circle at 2, shading between them.
Any of these are correct:
−4<x<2 , {x| −4<x<2 }
Write an inequality that represents this problem.
Riku wants to eat at least 2500 calories but no more than 3000 calories per day. He has already eaten a 475-calorie breakfast. Let x represent the number of calories Riku can eat for the rest of the day.
2500 ≤ |x + 475| ≤ 3000
OR if you put this:
x + 475 ≤ 3000 x + 475 ≥ 2500
What are the three possible numbers of solutions for an absolute value equation?
0, 1, or 2 solutions.
Solve 7x+4 ≤−10 OR 3x−9 ≥ 6
x≤−2 OR x≥5
How can this be written:
Closed circle at −3 shading left, closed circle at 5 shading right.
Any of these are correct:
x≤−3 OR x≥5 , {x| x≤−3 OR x≥5 }
If you chose this question....
your team loses 100 points...... :(
How many cases do we always have when solving absolute value?
Two cases: One positive, one negative but sign flips for negative case
Which would have NO Soultion?
A. x=5 AND x<5 B. x=5 OR x<5
A.
Show Picture:
Write an inequality that represents this graph AND explain why the circles are open or closed.
x>4 OR x ≤ 0
It is open at 4 because it's not the equal to sign, its closed at 0 because it has the equal to sign. They are facing different directions because it is an OR problem not an AND. AND means between, OR means different directions.
Write an inequality that represents this problem.
Juan needs to write an essay that has at least 300 words but no more than 500 words. He has already written 120 words. Let x represent the number of words Juan still needs to write.
300 ≤ |x + 120| ≤ 500
or if you said this:
x + 120 ≤ 500 x + 120 ≥ 300