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

Question

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

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

(

,

) 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:

(

,

)