Question

Use Vocabulary in Writing

Explain how many solutions the equations 2x + 1 = 2(x + 1) and 2x + 2 = 2 (x + 1)
have. Use vocabulary words in your explanation.

Answer 1

The first equation has no solution, while the second equation has infinite solutions.

Step-by-step explanation:

The two equations are: 2x + 1 = 2(x + 1) and 2x + 2 = 2(x + 1).

Simplifying the first equation, we distribute 2 to (x + 1) resulting in 2x + 1 = 2x + 2.

By subtracting 2x from both sides and simplifying, we get 1 = 2, which is a contradiction.

This means that the first equation has no solution.

For the second equation, we again distribute 2 to (x + 1) resulting in 2x + 2 = 2x + 2.

Notice that both sides of the equation are equal. This means that the second equation has infinite solutions.

Learn more about Solutions of Equations