What you have written, the "union" of two numbers, makes no sense at all. You take the union of sets, not numbers. You need intervals not numbers. The numbers you give, which are better written [itex]2+ \sqrt{3}[/tex] and [tex]2- \sqrt{3}[/tex], are where that left side is equal to 0. Then separate the intervals where it is true from the intervals where it is false. Take one value in each interval to see whether it is ">" or "<".RaDitZ said:Solve Inequalities with answers in Interval notation.
x^2 + 1 > 4x
Solve for x, U = Union
x^2 - 4x + 1 > 0
x= 3.732050808, 0.2679491924
Answer x= 3.732050808 U 0.2679491924 ?
Solving inequalities with interval notation involves finding the range of values that satisfy the inequality. To do this, you must first isolate the variable on one side of the inequality symbol. Then, depending on the direction of the inequality, you can either use a number line or interval notation to express the solution set.
Interval notation is a way to express a range of numbers using brackets or parentheses. The notation is written as [a,b] or (a,b), where a and b represent the lower and upper bounds of the interval, respectively. The brackets indicate that the number is included in the interval, while the parentheses indicate that the number is excluded.
In interval notation, brackets are used to indicate that the number is included in the interval, while parentheses are used to indicate that the number is excluded. To determine which one to use, you should look at the inequality symbol. If the inequality is greater than or equal to (≥) or less than or equal to (≤), then you use brackets. If the inequality is strictly greater than (>) or strictly less than (<), then you use parentheses.
Yes, it is possible to have both an open and closed interval in the same solution. For example, the solution to the inequality x > 3 could be expressed as (3, ∞), which includes all numbers greater than 3, but not 3 itself. Another example could be the solution to the inequality x ≤ 5, which could be expressed as (-∞, 5], including all numbers less than or equal to 5, but not any number less than -∞.
Yes, there are a few special cases when solving inequalities with interval notation. One example is when the solution set is a single value, in which case you would use a bracket on both ends of the interval. Another example is when the solution set is all real numbers, in which case you would use (-∞, ∞) or (-∞, ∞) depending on the direction of the inequality. Lastly, if the solution set is empty, then you would use the symbol ∅ to represent the empty set.