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What else can I help you with?
How do you check the solution to an equation?
plug your solution back into the original equation and work it out again
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 the solution to an equation?
a solution to an equation is the answer
What is an equation that has no solution called?
An equation that has no solution is called an equation that has no solution.
Why is it important to keep both sides of the equation equal?
If both sides of an equation are not equal, it won't be an equation any more! In solving equations, the strategy is to change both sides in the same way, so that an 'equivalent' equation is produced. An equivalent equation has the same solution as the original equation. You are aiming for an equation in which the variable is alone on one side. The quantity on the other side is the solution.
What is a solution of an eqaution derived from an original equation that is not a solution of the original equation?
Extraneous solution
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.
How do you check the solution to an equation?
plug your solution back into the original equation and work it out again
A solution that does not satisfy the original equation?
an extraneous solution.
What solution is a trial solution that takes not satisfy the original equation?
It is a trial solution, as mentioned in the question!
How can you tell that an equation has the same solution as the original equation?
If the two equations are linear transformations of one another they have the same solution.
How do you determine if a number is a solution of an equation?
plug your answer it to the original question
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 happens if you are checking a solution for the radical expression and find that it makes one of the denominators in the expression equal to zero?
Then it is not a solution of the original equation. It is quite common, when solving equations involving radicals, or even when solving equations with fractions, that "extraneous" solutions are added in the converted equation - additional solutions that are not solutions of the original equation. For example, when you multiply both sides of an equation by a factor (x-1), this is valid EXCEPT for the case that x = 1. Therefore, in this example, if x = 1 is a solution of the transformed equation, it may not be a solution to the original equation.
The solution to x equals -8?
x = -8 already is a solution. If an equation has been changed until the value of x is found, and this value is accurate to the original equation, then the equation has been solved.
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.
Why do you have to check the solutions when you have to solve radical equations?
Checking your solution in the original equation is always a good idea,simply to determine whether or not you made a mistake.If your solution doesn't make the original equation true, then it's wrong.
