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How is a extraneous solution of a ration equation similar to a excluded value of a rational equation?
An extraneous solution of a rational equation is a solution that arises from the algebraic process of solving the equation but does not satisfy the original equation. This can occur when both sides are manipulated in ways that introduce solutions not valid in the original context. An excluded value, on the other hand, refers to specific values of the variable that make the denominator zero, rendering the equation undefined. Both concepts highlight the importance of checking solutions against the original equation to ensure they are valid.
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How is an extraneous solution of a ration equation similar to an excluded value of a rational equation?
An extraneous solution of a rational equation is a solution that emerges from the algebraic process but does not satisfy the original equation, while an excluded value is a value that makes the denominator zero and is therefore not permissible in the equation. Both concepts highlight the limitations and constraints of rational expressions. Excluded values can lead to extraneous solutions if they are mistakenly included in the solution set. Thus, both are essential to consider when solving rational equations to ensure valid solutions.
What is a solution of an eqaution derived from an original equation that is not a solution of the original equation?
Extraneous solution
What is rational equation?
A rational equation is when its solution can be expressed as a fraction
What statement best describes the excluded values of a rational expression?
The excluded values of a rational expression are the values of the variable that make the denominator equal to zero. These values are not in the domain of the expression, as division by zero is undefined. To identify excluded values, set the denominator equal to zero and solve for the variable. Any solution to this equation represents an excluded value.
What does extraneous mean What must you do to determine whether a solution is an extraneous solution?
Extraneous means extra and unnecessary. Extraneous solutions are values that can arise from the process of solving the equation but do not in fact satisfy the initial equation. These solutions occur most often when not all parts of the process of solving are not completely reversible - for example, if both sides of the equation are squared at some point.
What is a solution of an eqaution derived from an original equation that is not a solution of the original equation?
Extraneous solution
A solution that does not satisfy the original equation?
an extraneous solution.
What is the extraneous solution to w equals sqrt 7w?
An "extraneous solution" is not a characteristic of an equation, but has to do with the methods used to solve it. Typically, if you square both sides of the equation, and solve the resulting equation, you might get additional solutions that are not part of the original equation. Just do this, and check each of the solutions, whether it satisfies the original equation. If one of them doesn't, it is an "extraneous" solution introduced by the squaring.
What is rational equation?
A rational equation is when its solution can be expressed as a fraction
Is one solution to a real-world problem involving a quadratic equation always extraneous?
No. Sometimes they are both extraneous.
What is an extraneous solution of an equation?
when you solve a questiom, you get an answer. If you chect your answer by substituting the value of the variable in the question and you don't get L.H.S and R.H.S equal then your answer is called extraneous solution.
What does extraneous mean What must you do to determine whether a solution is an extraneous solution?
Extraneous means extra and unnecessary. Extraneous solutions are values that can arise from the process of solving the equation but do not in fact satisfy the initial equation. These solutions occur most often when not all parts of the process of solving are not completely reversible - for example, if both sides of the equation are squared at some point.
If there is no solution to a system of equations it means?
extraneous solution. or the lines do not intersect. There is no common point (solution) for the system of equation.
What do you call the solution of a equation derived from an original equation that is not a solution of the original equation?
That's an extraneous solution. You need to check for these when algebraically solving equations, especially when you take both sides of an equation to a power.
Why is it necessary to check for extraneous solutions in radical equations?
1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
What is a extraneous solution?
A solution to an equation that you get at the end of whatever method you use that does not actually solve the original equation. One well-known example:1=2 ====>0=0 Therefore, one equals two.x0 x0The laws of algebra says that we can do this because we multiplied both sides by zero. Logically, we all know this isn't actually true. This is what extraneous solutions look like when solving linear equations:2x+3=9 If you assume x=1... 2(1)+3=9 ...and multiply everything by 0...0=0. Therefore, my guess is correct and x=1.
Does the equation 4x equals -20 have a solution over the set of rational numbers?
Yes, it does.
