Math

Question Solve an equation with a final step of 18=1818=18 and no variables. What is this type of equation called? Identity.

Studdy Solution

STEP 1

Assumptions
1. The equation in question is 18=1818=18.
2. All variables have been eliminated in the process of solving the equation.
3. We need to determine the term that describes this type of equation.

STEP 2

Understand the meaning of each term given in the options.
1. No Solution: This term is used when the equation has no solution, meaning there are no values for the variables that can satisfy the equation.
2. Identity: This term is used when the equation is true for all values of the variables involved. In other words, it is an identity if it is always true, regardless of the values of any variables that may appear in the equation.
3. Single Solution: This term is used when the equation has exactly one solution, meaning there is only one value for the variables that satisfies the equation.
4. Contradiction: This term is used when the equation is never true, no matter what values the variables take on.

STEP 3

Analyze the given equation 18=1818=18.
Since the equation 18=1818=18 is true for all values (even though no variables are present), and it does not depend on any variable, it is an identity. An identity is an equation that is always true, regardless of the values of any variables.

STEP 4

Choose the correct term based on the analysis.
The term that describes the equation 18=1818=18 is "Identity" because it is true for all possible values of variables, even though, in this case, the variables have been eliminated.
The correct term for this type of equation is "Identity".

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