When is an inequality all real numbers

Yes, that's right: you are looking for nonsense. If you come across an inequality that indicates information that is not true, then the inequality has no solution. Sometimes, it's possible to solve an inequality and realize it is meaningless! Let me give a couple of examples:. When solving an inequality, keep your eyes open for such scenarios where the answer you get makes no sense. You can get inequalities that are false for any variable.

These inequalities have no solution. You can also get inequalities that are true for any variable. These have an infinite number of solutions. Here we get a true statement. So we know this inequality's solution is all real numbers or infinite solutions. No matter what number you put in for p, you get a true statement.

This means the inequality has no solutions. The absolute value of a number is never negative. The absolute value of 5 is 5. How do you know if an absolute value inequality has no solution? Okay, if absolute values are always positive or zero there is no way they can be less than or equal to a negative number. Therefore, there is no solution for either of these.

In this case if the absolute value is positive or zero then it will always be greater than or equal to a negative number. How do you solve and inequality? To solve a compound inequality, first separate it into two inequalities.

Determine whether the answer should be a union of sets "or" or an intersection of sets "and". Then, solve both inequalities and graph. How can you tell if an inequality will have a solid line? Graphing Inequalities. The first interval must indicate all real numbers less than or equal to 1. However, we want to combine these two sets.

When we work with inequalities, we can usually treat them similarly to but not exactly as we treat equations. We can use the addition property and the multiplication property to help us solve them. The one exception is when we multiply or divide by a negative number, we must reverse the inequality symbol. The addition property for inequalities states that if an inequality exists, adding or subtracting the same number on both sides does not change the inequality.

As the examples have shown, we can perform the same operations on both sides of an inequality, just as we do with equations; we combine like terms and perform operations.

To solve, we isolate the variable.