Diego and Jada are both trying to write an expression with fewer terms that is equivalent to:
Jada thinks is equivalent to the original expression.
Diego thinks is equivalent to the original expression.
We can show that expressions are equivalent by writing out all the variables. Explain or show why each expression (after the first row) is equivalent to the one before it.
Here is another way we can rewrite the expressions. Explain or show why each expression (after the first row) is equivalent to the one before it.
3.3
Activity
Making Sides Equal
Replace each ? with a term or expression in parentheses that will make the expression on the left side of the equation equivalent to the expression on the right side. Check your results for Set A with your partner and work to reach an agreement before moving on to Set B.
Set A
Set B
Student Lesson Summary
There are many ways to write equivalent expressions, and they may look very different from each other. One way to determine if two expressions are equivalent or not is to substitute the same number for the variable in both expressions.
For example, when is 1, the expression equals 4 and the expression equals 7. This means and are not equivalent.
If two expressions are equal when many different values are substituted for the variable, then the expressions may be equivalent—it is impossible to compare the two expressions for all values. To know for sure, we use properties of operations. For example, is equivalent to because:
Glossary
None
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