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Learning Targets

• I am aware of some common pitfalls when writing equivalent expressions, and I can avoid them.
• When possible, I can write an equivalent expression that has fewer terms.

Combining like terms allows us to write expressions more simply with fewer terms. But it can sometimes be tricky with long expressions, parentheses, and negatives. It is helpful to think about some common errors that we can be aware of and try to avoid:

• 6x - x is not equivalent to 6. While it might be tempting to think that subtracting x makes the x disappear, the expression is really saying take 1x away from 6x 's, and the distributive property tells us that 6x - 6 is equivalent to (6 - 1)x.
• 7- 2x is not equivalent to 5x. The expression 7 - 2x tells us to double an unknown amount and subtract it from 7. This is not always the same as taking 5 copies of the unknown.
• 7 - 4(x + 2) is not equivalent to 3(x + 2). The expression tells us to subtract 4 copies of an amount from 7, not to take (7 - 4) copies of the amount.

If we think about the meaning and properties of operations when we take steps to rewrite expressions, we can be sure we are getting equivalent expressions and are not changing their value in the process.

Some students are trying to write an expression with fewer terms that is equivalent to 8 - 3(4 - 9x).

1. Do you agree with any of them? Explain your reasoning.
2. For each strategy that you disagree with, find and describe the errors.

*HINT* Writing subtraction as “adding the opposite” will help prevent mistakes when writing equivalent expressions!

Select all expressions that are equivalent to 16x - 12 - 24x + 4. Show or explain your reasoning.

• 4 + 16x - 12(1 + 2x)
• 40x - 16
• 16x - 24x - 4 + 12
• -8x - 8

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