Answer:
( − ∞ , ∞ ) hope i help
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:
( − ∞ , ∞ )