How do you solve and write the following in interval notation: #7 ≥ 2x − 5# OR #(3x − 2) / 4>4#?
First, solve each inequality. I'll solve the first one first.
Therefore, x could be any number less than or equal to 6. In interval notation, this looks like:
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
Let's try the second example:
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:
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