10 + 3x < 4 or 2x + 5 > 11 in interval notation​

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10 + 3x < 4 or 2x + 5 > 11 in interval notation​

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Thu Giang 5 months 2021-08-23T09:52:13+00:00 1 Answers 3 views 0

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    0
    2021-08-23T09:54:03+00:00

    Answer:

    (


    ,

    ) hope i help

    Step-by-step explanation:

    First, solve each inequality. I’ll solve the first one first.

    7

    2
    x

    5

    12

    2
    x

    6

    x

    Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:

    (


    ,
    6
    ]

    The parenthesis means that the lower end is not a solution, but every number above it is. (In this case, the lower end is infinity, so a parenthesis must be used, since infinity is not a real number and so it cannot be a solution.) The bracket means that the upper end is a solution. In this case, it indicates that not only could  

    x

    be any number less than 6, but it could also be 6.

    Let’s try the second example:

    3
    x

    2
    4
    >
    4

    3
    x

    2
    >
    16    3
    x
    >
    18
    x
    >
    6

    Therefore, x could be any number greater than 6, but x couldn’t be 6, since that would make the two sides of the inequality equal. In interval notation, this looks like:

    (
    6
    ,

    )  

    The parentheses mean that neither end of this range is included in the solution set. In this case, it indicates that neither 6 nor infinity are solutions, but every number in between 6 and infinity is a solution (that is, every real number greater than 6 is a solution).

    Now, the problem used the word “OR”, meaning that either of these equations could be true. That means that either  x  is on the interval  (


    ,
    6
    ]
    or the interval  (
    6
    ,

    )

    . In other words,  x

    is either less than or equal to 6, or it is greater than 6. When you combine these two statements, it becomes clear that  

    x

    could be any real number, since no matter what number  

    x

    is, it will fall in one of these intervals. The interval “all real numbers” is written like this:

    (


    ,

    )

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