Compound Inequalities, Intersections - Definition
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- (Videos) Compound Inequalities by mathman1024 This video by mathman1024 works through problems with compound inequalities. Summary\large{\text{Summary}}Summary There are two typ…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Solving Compound Inequalities with an Intersection (AND) In previous lessons, we saw how to solve individual inequalities, with grouping and graphing. In this lesson, we're goin…
By Anusha Rahman
- Solve Compound Inequality for Intersection (AND) To solve AND/Intersection compound inequalities, first solve each inequality separately. Then combine your inequalities together…
By Caroline K
Problems 30
- Which of the following compound inequalities is equivalent to −2x<−5q<−8-2x < -5q < -8−2x<−5q<−8?
- Which of the following points are solutions to the inequality x−3<y≤x+3x-3 < y \leq x + 3x−3<y≤x+3?
- What is the solution to the following inequalities? 7<3x+12x≤16\begin{align} 7&<3x+1 \\ 2x&\leq16 \end{align}72x<3x+1≤16
- Solve the following compound inequality. 7x>−5 and x>87x>-5\text{ and }x>87x>−5 and x>8
- Solve the following compound inequality. −6x≥4 and −x≥−3-6x\geq4\text{ and }-x\geq-3−6x≥4 and −x≥−3
- Solve the following compound inequality. 6x≥−14 and −6x>−76x\geq-14\text{ and }-6x>-76x≥−14 and −6x>−7
- Solve the following compound inequality. 2x≥8 and −x≤62x\geq8\text{ and }-x\leq62x≥8 and −x≤6
- 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
- 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 …
- Find all real numbers such that x≥0x\ge0x≥0 and x<4x\sqrt x < 4xx<4x.
- Which of the following compound inequalities is equivalent to 2x−3<x+y≤2x+32x-3 < x + y \leq 2x + 32x−3<x+y≤2x+3?
- Simplify −4<4x<4-4 < 4x < 4−4<4x<4. (Hint: You can divide across the whole inequality.)
- Find all real numbers xxx such that x<0x < 0x<0 AND x2+x>4xx^2 + x > 4xx2+x>4x.
- Graph the following compound inequalities and select the one that matches the graph above.
- Which interval expresses the overlap between x>2x > 2x>2 and x<5x < 5x<5?
- Which interval expresses the overlap between x≥−2x \ge -2x≥−2 and x<0x < 0x<0?
- What is the intersection of the sets described by the inequalities x≤3x \le 3x≤3 and x>−3x > -3x>−3?
- What is the intersection of the sets described by the following inequalities: x≤−1 and x>1x \le -1 \text{ and } x > 1x≤−1 and x>1
- Miranda and Monique are ordering flowers for an event they are planning. Miranda tells the florist that they will need at least 50 flowers, but no more than 75. However, Monique…
- Cassandra is throwing a birthday party for her friend Danny. She was hoping to invite somewhere between 151515 and 303030 friends (inclusive), but Danny is shy and asks her to i…
- Andy, Leslie, and Donna are trying to schedule a meeting at a time that works for everyone. Andy is free from 8:00 AM-11:00 AM, Leslie is free from 7:00 AM-10:30 AM, and Donna i…
- Solve for xxx: 5x−2>0and2x−1<35x - 2 > 0 \hspace{0.25 in} \text{and} \hspace{0.25 in} 2x -1 < 35x−2>0and2x−1<3
- Which is not a solution to: −3≤2x+1≤7-3 \leq 2x+1 \leq 7−3≤2x+1≤7
- Solve the compound inequality: 3x−9<2x+10 and 5+7x≤10x−103x - 9 < 2x + 10 \,\,\text{and}\,\, 5 + 7x \leq 10x - 103x−9<2x+10and5+7x≤10x−10
- What kind of mathematical graph would I want to use to show that two inequalities share common elements?
- What inequality is represented by the number line above?
- What compound inequality represents the number line above?
- Which inequality corresponds to the graph above?
- 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?