Interval and Set-Builder Notation - Compound Inequalities
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- Interval Notation and Set-Builder Notation for Intervals Earlier, we learning about writing inequalities. We saw how to graph linear inequalities. Now, we'll look at intervals, …
By Brian Chen, Victor Wang, Jonathan Heller, Caroline K, Anusha Rahman
- (Video) Linear Inequality Interval Notation by mathman1024 This video by mathman1024 goes over interval notation. Summary You find the bounds of the solution and put them in bet…
By Alex Federspiel, Joshua Siktar, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Interval Notation for Compound Inequality We can use interval notation to represent the solutions of a compound inequality. Before we see how, let's review interval notation. AN…
By Caroline K
Problems 38
- Convert this compound inequality to interval notation. x>2 and x≤8x>2\text{ and }x\leq8x>2 and x≤8
- Convert this compound inequality to interval notation. x<2 and x<18x<2\text{ and }x<18x<2 and x<18
- Convert this compound inequality to interval notation. x<−5 or x≥−2x<-5\text{ or }x\geq-2x<−5 or x≥−2
- Convert this compound inequality to interval notation. x<2 or x<18x<2\text{ or }x<18x<2 or x<18
- Convert this compound inequality to interval notation. x<−10 or x<−3x<-10\text{ or }x<-3x<−10 or x<−3
- Convert this compound inequality to interval notation. x<10 and x≤−10x<10\text{ and }x\leq-10x<10 and x≤−10
- Convert this compound inequality to interval notation. x>3 and x<−7x>3\text{ and }x<-7x>3 and x<−7
- Convert this compound inequality to interval notation. x>3 or x<−7x>3\text{ or }x<-7x>3 or x<−7
- Solve the following compound inequality. −x≤−4 or 6x<7-x\leq-4\text{ or }6x<7−x≤−4 or 6x<7
- Solve the following compound inequality. −7x>−8 or −x>7-7x>-8\text{ or }-x>7−7x>−8 or −x>7
- Solve the following compound inequality. 9x≥7 or 6x>49x\geq7\text{ or }6x>49x≥7 or 6x>4
- Solve the following compound inequality. −4x≤−8 or 2x≤16-4x\leq-8\text{ or }2x\leq16−4x≤−8 or 2x≤16
- Solve the following compound inequality. 10x<7 or −6x≤−1410x<7\text{ or }-6x\leq-1410x<7 or −6x≤−14
- Solve the following compound inequality. −5x≤−2 or −2x≤−8-5x\leq-2\text{ or }-2x\leq-8−5x≤−2 or −2x≤−8
- Solve the following compound inequality. 3x>19 and 9x<−173x>19\text{ and }9x<-173x>19 and 9x<−17
- Solve the following compound inequality. 4x<−14 and 6x≤−134x<-14\text{ and }6x\leq-134x<−14 and 6x≤−13
- At most, how many regions on a line do 101010 points create? (Alternative formulation: Using only 101010 vertical cuts, how many pieces can you slice a horizontal rope into?)
- Let xxx be a real number greater than −3-3−3. If (−3,x)∩(6−2x,12)=∅(-3, x) \cap (6-2x, 12) = \varnothing(−3,x)∩(6−2x,12)=∅, what is the largest possible value of xxx? Note that …
- Which symbols represents a closed set?
- Which symbols represents an open set?
- Represent the following statement mathematically, "All values between −5-5−5 and 555, including −5-5−5, but not including 555."
- Represent the following statement mathematically, "All values between −3-3−3 and 333, including −3-3−3 and 333."
- What is the range of the function in interval notation?
- Express the given inequality in interval notation: x≥−2x\geq{-2}x≥−2
- The interval notation for all real numbers is
- Which of the following intervals contains only negative numbers?
- Say you decided to enroll for one month to try this out. Let xxx be the number of classes you are taking in this month and let yyy be the money you spent this month. What is a r…
- What inequality is the above number line depicting?
- Express the given compound inequality in interval notation: x≤9 and x>−5x \leq 9\text{ and } x > -5x≤9 and x>−5
- When buying furniture, Max learns that the tables he likes cost between 100\100100 and 300\300300 inclusive and the lamps he likes cost between 20\2020 and 50\5050 inclusive. Wh…
- Is [0,1)[0,1)[0,1) an open or closed interval?
- Which of the following is an open interval? Select all that apply.
- If I want to say that a number line includes all numbers from 333 to 141414, including both 333 and 141414, what interval notation would this be?
- What is the interval notation for the line above?
- If I want to depict that a number is included in at the end of an interval, what type of bracket would I use?
- Which inequality represents all xxx that are in the interval (−∞,0)(-\infty, 0)(−∞,0) and in the interval (−∞,0](-\infty, 0](−∞,0]?
- Two sides of a triangle have lengths 444 and 14.14.14. What is the range of possible values of the semiperimeter of the triangle?
- The Pittsburgh Pirates play the St. Louis Cardinals on April 1, 2019 (see here for more info). Let's say the probability of the Pirates winning this game is PPP. Then we define …