There are three possible outcomes for compound inequalities joined by the word and:
- The solution could be all the values between two endpoints.
- The solution could begin at a point on the number line and extend in one direction.
- In cases where there is no overlap between the two inequalities, there is no solution to the compound inequality.
How do you solve a compound inequality?
To solve an inequality, we can:
- Add the same number to both sides.
- Subtract the same number from both sides.
- Multiply both sides by the same positive number.
- Divide both sides by the same positive number.
- Multiply both sides by the same negative number and reverse the sign.
Why do some equations or inequalities have no solution?
Some equations do not have any solution because they show an impossible situation. Or better we can say that an equation which have no solution means its solution is not a well defined proper number ( impossible number). or {1 = 0} Which is impossible…. so, the solution set is not possible.
Which system of inequalities has no solution?
If there is no intersection region, then we conclude the system of inequalities has no solution. Let’s go over a couple of examples to understand these steps. Example 1. Graph the following system of linear inequalities: y ≤ x – 1 and y < –2x + 1. Solution. Graph the first inequality y ≤ x − 1.
How do you write a compound inequality?
What are some examples of inequalities?
- Wage Inequality. …
- Homelessness. …
- Occupational Sex Segregation. …
- Racial Gaps in Education. …
- Racial Discrimination. …
- Child Poverty. …
- Residential Segregation. …
- Health Insurance.
What is an example of a no solution inequality?
2:373:40Solving Inequalities with No Solution or Infinite Solutions - YouTubeYouTubeStart of suggested clipEnd of suggested clipSo the like terms I have are 3x plus 10 greater than 3x plus 18. Well I notice these three X's areMoreSo the like terms I have are 3x plus 10 greater than 3x plus 18. Well I notice these three X's are the same so when I subtract 3x from both sides they'll go away. And I'm left with 10 is greater than
How do you determine if an inequality is no solution?
Isolate the absolute value expression on the left side of the inequality. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.
What are the solutions of the compound inequality?
The solution of a compound inequality that consists of two inequalities joined with the word and is the intersection of the solutions of each inequality. In other words, both statements must be true at the same time.
Which absolute value inequality has no solution?
If the absolute value is less than or less than or equal to a negative number, there is no solution.
What does no solution mean?
The solution x = 0 means that the value 0 satisfies the equation, so there is a solution. “No solution” means that there is no value, not even 0, which would satisfy the equation. Also, be careful not to make the mistake of thinking that the equation 4 = 5 means that 4 and 5 are values for x that are solutions.
What is a compound inequality give some examples?
Compound inequalities are the derived form of inequalities, which are very useful in mathematics whenever dealing with a range of possible values. For example, after solving a particular linear inequality, you get two solutions, x > 3 and x < 12. You can read it as “3 is less than x, which is less than 12.
How do you know if a compound inequality is and or OR?
A compound inequality (or combined inequality ) is two or more inequalities joined together with or or and . To be a solution of an or inequality, a value has to make only one part of the inequality true. To be a solution of an and inequality, it must make both parts true. (In other words, x≥−1 and x<2 .)
What's a compound inequality in math?
A compound inequality is an inequality that combines two simple inequalities.
Why do some inequalities have no solution?
Some inequalities do not have a solution. When two inequalities have parallel lines and the shaded areas do not overlap (i.e., the opposite areas are shaded), then the system has no solution. This means that there is no coordinate point that makes both inequalities true.
What makes an absolute value no solution?
Since the absolute value of any number other than zero is positive, it is not permissible to set an absolute value expression equal to a negative number. So, if your absolute value expression is set equal to a negative number, then you will have no solution.
What is common for the equations that have no solution?
The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.
What is an example of a no solution equation?
The last type of equation is known as a contradiction, which is also known as a No Solution Equation. This type of equation is never true, no matter what we replace the variable with. As an example, consider 3x + 5 = 3x - 5. This equation has no solution.
What does no solution look like?
When a problem has no solution you'll end up with a statement that's false. For example: 0=1 This is false because we know zero can't equal one. Therefore we can conclude that the problem has no solution.
What is the condition for no solution?
If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. This type of system of equations is called an inconsistent pair of linear equations. If we plot the graph, the lines will be parallel and system of equations have no solution. Example.
How do you know if an inequality has infinite solutions?
Inequalities that produce a false statement have no real solutions. Inequalities that hold true for all values have infinite solutions.
Can An Inequality Have No Solution?
An inequality can have no solution, and there are several cases where this can happen, including:
Can An Inequality Have Only One Solution?
An inequality can have only one solution (that is, a single real value of x as the only solution). This can happen with any of the above-mentioned inequalities: absolute, compound, and quadratic.
Can An Inequality Have An Equal Sign?
An inequality can have an equal sign (>= or <=), as we saw in the earlier examples. This just means that we include the endpoint as a solution of the inequality.
Can An Inequality Equal Zero?
An inequality can equal zero in some cases. This can happen if zero is in the solution set (such as x < 1) or if zero is one of the endpoints for an inequality with an equal sign (such as x >= 0).
How Can The Solution Set For An Inequality Be All Real Numbers?
The solution set for an inequality can be all real numbers in several cases. These should be familiar from our earlier discussion:
Conclusion
Now you know how an inequality can have no solution, one solution, or all real numbers as its solution set. You also have some examples to help you see when these cases can occur.
What is Compound Inequality?
There are other cases where you can use inequality to represent more than one constraining value. In such situations, a compound inequality is applied.
How to Solve Compound Inequalities?
The solution for compound inequalities depends on whether the words “and” or “or” are used to connect the individual statements.