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.

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asked Mar 26, 2024 88.6k views

1 Answer

Logan Ding · Answer 1 · 2024-03-31T16:10:33+0000

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

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.