Question

Is it possible to make an equation from these two equations? If so, do they have infinite solutions, no solutions, or one solution?

Consider the mathematical sentence 2 = 2.

Is there any variable or constant that you could add to or subtract from both sides, or multiply or divide both sides by using the Properties of Equality to make this true sentence false? Choose variables and constants to create new mathematical sentences to justify your conclusion


Consider the mathematical sentence 2 ≠ 3.

Is there any variable or constant that you could add to or subtract from both sides, or

multiply or divide both sides by using the Properties of Equality to make both sides equal? Choose variables and constants to create new mathematical sentences to justify your conclusion.

Answer 1

For the equation 2 = 2, it is not possible to make this equation false by using the Properties of Equality. This is because the equation is already true, and any manipulation of the equation using the Properties of Equality would not change this fact. Therefore, this equation has one solution.

For the equation 2 ≠ 3, it is not possible to make both sides equal by using the Properties of Equality. This is because the equation is stating that the two sides are not equal, and any manipulation of the equation using the Properties of Equality would not change this fact. Therefore, this equation has no solutions.