Question

How do you know whether an equation is an​ identity? How many solutions does an identity​ have? Explain. Choose the correct answer below.

A. An equation is an identity if it can be rewritten as 0=0. Such an equation has only one​ solution, 0, and that is the identity of the variable.

B. An equation is an identity if it can be rewritten as an equation of the form ​"variable​number," such as x5 or y3. Such an equation has only one​ solution, and the solution is called the identity of the variable.

C. An equation is an identity if it can be rewritten as an equation of the form ​"variable​number," such as x5 or y3. Such an equation has an infinite number of solutions because a variable can be any number.

D. An equation is an identity if it can be rewritten as 0=0. Such an equation has an infinite number of solutions because it reduces to a true statement regardless of the value of the variable.

Answer 1

• Option D

Explanation:

A. An equation is an identity if it can be rewritten as 0=0. Such an equation has only one​ solution, 0, and that is the identity of the variable.

• Incorrect. In this case there are infinite solutions.

B. An equation is an identity if it can be rewritten as an equation of the form ​"variable​number," such as x5 or y3. Such an equation has only one​ solution, and the solution is called the identity of the variable.

• Incorrect. There might be more than one solution and the equation is not an identity.

C. An equation is an identity if it can be rewritten as an equation of the form ​"variable​number," such as x5 or y3. Such an equation has an infinite number of solutions because a variable can be any number.

• Incorrect. There might be one or no solution and the equation is not an identity.

D. An equation is an identity if it can be rewritten as 0=0. Such an equation has an infinite number of solutions because it reduces to a true statement regardless of the value of the variable.

• Correct