Question

Jorge simplified an expression correctly to get -2x -2. What could Jorge's expression be?

Answer 1

Jorge simplified an expression to -2x - 2 by possibly combining like terms or distributing a negative sign through parentheses. He could have started with expressions like (-2x + 3) - 5, -4x + 2x - 2, or (-x - 1) - (x + 1), and applied basic algebraic principles to simplify them correctly.

Step-by-step explanation:

If Jorge simplified an expression correctly to get -2x - 2, there are several possible original expressions he could have started with. One key idea with simplifying expressions is to combine like terms and apply the distributive property if necessary.

• (-2x + 3) - 5: Here, Jorge would combine like terms by subtracting 5 from 3, resulting in -2.
• -4x + 2x - 2: Applying the combination of like terms, the x terms would simplify to -2x.
• (-x - 1) - (x + 1): Distributing the negative sign through the second set of parentheses and then combining like terms would also result in -2x - 2.

When simplifying expressions, it's important to remember the basic principles of algebra:

1. Combining like terms, which involves adding or subtracting coefficients of the same variable.
2. The distributive property, which allows us to remove parentheses by multiplying the term outside the parentheses by each term inside.
3. Changing the signs when subtracting a negative number; for example, subtracting -6 from 2 gives us 2 + 6 = 8.
4. Multiplying and dividing numbers while paying attention to the signs, as the product or quotient of two numbers with different signs will always be negative.

Using these principles, you can arrive at -2x - 2 from a variety of expressions.