The set of all numbers that make an inequality true is known as the solution set. It consists of all the values of the variable that satisfy the given inequality. This set can be expressed using interval notation or set builder notation, depending on the context of the problem. The solution set is crucial in determining the range of values that satisfy the given conditions.
To determine which values from the set {1, 2, 3, 4, 5} make the inequality n < 26 true, we need to find all numbers in the set that are less than 26. In this case, the values that satisfy the inequality are 1, 2, 3, 4, and 5. Therefore, the values from the set {1, 2, 3, 4, 5} that make the inequality n < 26 true are 1, 2, 3, 4, and 5.
x ≥ 6
Yes.
That is how an identity is defined. If the solution was not true for all numbers, then it would not be called an identity. In fact, it should be true for all complex numbers as well.
True.
It means to find all the numbers for which the inequality is true.
To determine which values from the set {1, 2, 3, 4, 5} make the inequality n < 26 true, we need to find all numbers in the set that are less than 26. In this case, the values that satisfy the inequality are 1, 2, 3, 4, and 5. Therefore, the values from the set {1, 2, 3, 4, 5} that make the inequality n < 26 true are 1, 2, 3, 4, and 5.
The solution of an inequality is a set of values that satisfy the inequality condition. For example, in the inequality ( x > 3 ), the solution includes all numbers greater than 3, such as 4, 5, or any number approaching infinity. Solutions can be expressed as intervals, such as ( (3, \infty) ), or as a number line representation. These solutions help identify the range of values that make the inequality true.
Not unless you have an infinite amount of time as there are an infinite amount of numbers that are solutions to an inequality.
Since it is an inequality, there is no way to solve for x. It equals all real numbers.
Yes, it is true.
that would be limited to 3 and -3 for values of x
x ≥ 6
If both sides of an inequality are multiplied or divided by the same positive number, the direction of the inequality symbol remains the same. For example, if you have ( a < b ) and you multiply both sides by a positive number ( c ), the inequality remains ( ac < bc ). This property holds true for all positive numbers, ensuring the relationship between the two sides is preserved.
The statement "X0" is unclear, but if you are referring to an inequality such as x > 0 or x ≤ 0, it indicates that there are infinite solutions within the specified range. For instance, if the inequality is x > 0, the solutions include all positive real numbers. These solutions can be represented on a number line or in interval notation, such as (0, ∞) for x > 0.
I assume you have inequalities that involve variables. If you replace the variable by some number, you will get an inequality that is either true or false. A value for the variable that results in a true statement is said to "satisfy" the inequality. For example, in: x + 3 > 10 If you replace x by 8, you get a true statement, since 11 is greater than 10; if you replace x by 7, you get a false statement, since 10 is not greater than 10. In this case, there are two inequalities; you have to find all numbers that satisfy both inequalities; in other words, that convert both inequalities into true statements.
The inequality ( x - 2 > 0 ) can be solved by adding 2 to both sides, resulting in ( x > 2 ). Thus, the solutions to the inequality are all real numbers greater than 2. In interval notation, this is expressed as ( (2, \infty) ).