Compound Inequalities, Union - Definition & Examples
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- (Video) Writing OR Compound Inequalities Using Interval Notation by PatrickJMT This video by PatrickJMT covers "or" compound inequalities. Summary\large{\text{Summary}}Summary A…
By Alex Federspiel, Zora Gilbert, Joshua Siktar, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Solving Linear Compound Inequalities Compound inequalities involve two separate parts. Some inequality statements require you to find solutions that work in both parts. These ar…
By Alex Federspiel, Jonathan Heller, Amy Feraco, Caroline K, Anusha Rahman
- Solving OR Inequalities Earlier, we saw how to solve AND inequalities, with the solution being the intersection of two inequalities. Now, we'll look at OR inequalities. To solve…
By Caroline K, Anusha Rahman
Problems 27
- Find the solution to the following inequalities. 6+x≥4 or 9+x<4\begin{gather} 6+x\geq4\\ \text{ or } \\ 9+x<4 \end{gather}6+x≥4 or 9+x<4
- 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
- Graph each of the compound inequalities on a number line and see which one matches the graph above.
- Adrea and Allison were shopping for shoes when they found a pair that they both wanted to try on. Adrea can wear any of the sizes between 7.5 and 8.5 (inclusive), and Allison ca…
- Antonio and Lucio were shopping for shoes when they found a pair that they both wanted to try on. Antonio can wear any of the sizes between 8 and 9.5 (inclusive), and Lucio can …
- Andy and Selena are at a carnival when they come across a guessing game. A big jar is filled to the top with gumballs, and the goal is to guess how many gumballs are in the jar.…
- Shia and Leslie are at a carnival when they come across a guessing game. A big jar is filled to the top with M&M's, and the goal is to guess how many M&M's are in the jar. \\ Sh…
- What is a better way to write, 5≤x≤15 or 12≤x≤185\le x \le 15 \text{ or } 12\le x \le 185≤x≤15 or 12≤x≤18?
- A (fictional) species is highly adaptable to extreme temperatures, but cannot live in moderate temperatures. This species can live through temperatures less than −10∘-10^{\circ}…
- A species of koala can only live in moderate temperatures. To survive, the temperature must be greater than 10∘10^{\circ}10∘C and less than 30∘30^{\circ}30∘C. How would you expr…
- Find the interval representation for xxx values that satisfy the following compound inequality: 5x<15 or 3x>365x<15 \text{ or }3x>365x<15 or 3x>36
- Find the interval representation for xxx values that satisfy the following compound inequality: 6x>42 or 3x<126x>42 \text{ or }3x<126x>42 or 3x<12
- Which is the compound inequality expressing (−∞,2)∪(3,∞)(-\infty,2)\cup(3,\infty)(−∞,2)∪(3,∞)?
- Which is the compound inequality expressing (−∞,15]∪[45,∞)(-\infty,15]\cup[45,\infty)(−∞,15]∪[45,∞)?
- How do you express the compound inequality x>10x>10x>10 or x<5x<5x<5 in interval notation?
- How do you express the compound inequality x≥3x\ge3x≥3 or x≤−3x\le-3x≤−3 in interval notation?
- Solve the following compound inequality. 5−7x≥12 or 3x−2<75-7x \ge 12 \text { or } 3x-2 < 75−7x≥12 or 3x−2<7
- Find all values of xxx such that 3x−1<8 or x−5<0.3x - 1 < 8 \quad \text { or } \quad x-5<0.3x−1<8 or x−5<0.
- Solve for yyy in the following compound inequality. 2y+7<13or−3y−2≤102y+7 < 13 \quad \text{or}\quad -3y-2 \le 102y+7<13or−3y−2≤10
- Solve for xxx in the following compound inequality. 3x−1<8 or x−5>03x-1 < 8 \quad \text{ or } \quad x-5 > 03x−1<8 or x−5>0
- Solve for xxx in the following compound inequality. x+2>5orx+4<5x+2 > 5 \quad \text{or} \quad x+4 < 5x+2>5orx+4<5
- Solve the compound inequality: x−2<−8 or x8>1x - 2 < -8 \,\,\text{or}\,\, \frac{x}{8} > 1x−2<−8or8x>1