What graph represents the compound inequality x<5/4 or x>5/2
2 answers:
Answer:
SECOND graph.
Step-by-step explanation:
Given compound inequality,
![x \leq \frac{5}{4}\text{ or }x \geq \frac{5}{2}](https://tex.z-dn.net/?f=x%20%5Cleq%20%5Cfrac%7B5%7D%7B4%7D%5Ctext%7B%20or%20%7Dx%20%5Cgeq%20%5Cfrac%7B5%7D%7B2%7D)
![\because \frac{5}{4}=1.25\text{ or }\frac{5}{2}=2.5](https://tex.z-dn.net/?f=%5Cbecause%20%5Cfrac%7B5%7D%7B4%7D%3D1.25%5Ctext%7B%20or%20%7D%5Cfrac%7B5%7D%7B2%7D%3D2.5)
![\implies x \leq 1.25\text{ or }x\geq 2.5](https://tex.z-dn.net/?f=%5Cimplies%20x%20%5Cleq%201.25%5Ctext%7B%20or%20%7Dx%5Cgeq%202.5)
If x ≥ 1.25
In the number line closed circle on 1.25 and shaded left side from 1.25,
If x ≤ 2.5
In the number line closed circle on 2.5 and shaded right side from 2.5
Hence, SECOND option is correct.
For this case we have to:
: Represents all values less than or equal to![\frac {5} {4}.](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%7D%20%7B4%7D.)
: Represents all values greater than or equal to ![\frac {5} {2}.](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%7D%20%7B2%7D.)
As the inequalities include the sign "=", then the borders of the graphs will be closed.
![\frac {5} {4} = 1.25\\\frac {5} {2} = 2.5](https://tex.z-dn.net/?f=%5Cfrac%20%7B5%7D%20%7B4%7D%20%3D%201.25%5C%5C%5Cfrac%20%7B5%7D%20%7B2%7D%20%3D%202.5)
The word "or" indicates one solution or the other, so the correct option is graph B
ANswer:
Option B
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Answer:
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Step-by-step explanation:
![\frac{1}{2} ( \frac{2}{3} + \frac{3}{4}) \\ = \frac{1}{2} ( \frac{2 \times 4}{3 \times 4} + \frac{3 \times 3}{4 \times 3} ) \\ = \frac{1}{2} ( \frac{8}{12} + \frac{9}{12} ) \\ = \frac{1}{2} ( \frac{8 + 9}{12} ) \\ = \frac{1}{2} ( \frac{17}{12} ) \\ = \frac{1 \times 17}{2 \times 12} \\ = \frac{17}{24}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%5Cfrac%7B2%7D%7B3%7D%20%20%2B%20%20%5Cfrac%7B3%7D%7B4%7D%29%20%5C%5C%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%20%28%20%5Cfrac%7B2%20%5Ctimes%204%7D%7B3%20%5Ctimes%204%7D%20%20%2B%20%20%5Cfrac%7B3%20%5Ctimes%203%7D%7B4%20%5Ctimes%203%7D%20%29%20%5C%5C%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%5Cfrac%7B8%7D%7B12%7D%20%20%2B%20%20%5Cfrac%7B9%7D%7B12%7D%20%29%20%5C%5C%20%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%5Cfrac%7B8%20%2B%209%7D%7B12%7D%20%29%20%5C%5C%20%20%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%28%20%5Cfrac%7B17%7D%7B12%7D%20%29%20%5C%5C%20%20%3D%20%20%5Cfrac%7B1%20%5Ctimes%2017%7D%7B2%20%5Ctimes%2012%7D%20%20%5C%5C%20%20%3D%20%20%5Cfrac%7B17%7D%7B24%7D%20)
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Answer:
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Step-by-step explanation: