Algebra Class: Equivalent Expressions

Which statements are true for the expressions 5 + 3x - 2 and x + 2(x + 1) + 1 when x = 3 and x = 7? (Check all that apply)

Which statements are true for the expressions 7x + 4 and 3x + 5 + 4x - 1 when x = 4 and x = 6? (Check all that apply)

Which expression is equivalent to 7(xy)?

Which expressions are equivalent to 8.9x + 6.2 + 8.7? (Check all that apply)

Which expressions are equivalent when m = 1 and m = 4?

What proves that the expressions 4(x + 3) + 2 and 6(x + 2) are equivalent?

What describes the correct method to determine if 4x - x + 5 and 8 - 3x - 3 are equivalent?

Which expressions are equivalent to g + h + (j + k)? (Check all that apply)

Did Vance apply the associative property correctly in (4.5m + 7/8) - 9 as 4.5m(7/8 - 9)?

What property was applied to create the equivalent expression 7x + (5 + 6x) -----> (7x + 5) + 6x?

Equivalent Expressions

Equivalent expressions have the same value for any specific value of the variable involved, such as x or m.
For x=3 and x=7:
- Expressions 5 + 3x - 2 and x + 2(x + 1) + 1 are equivalent since both yield the same result, specifically for x + 6.
- Both expressions evaluate to 33 when x=10.
For x=4 and x=6:
- Expressions 7x + 4 and 3x + 5 + 4x - 1 are found to be equivalent.
- Their values equal 18 when x=2, and they maintain equivalence at x=8.
The expression 7(xy) can be equivalent to x(7y) due to the commutative property of multiplication.

Expressions Simplification

The expression 8.9x + 6.2 + 8.7 can be simplified equivalently to:
- 8.9x + 8 - 7 + 6.2
- 8.7 + 8.9x + 6.2
- 6.2 + 8.7 + 8.9x

Determining Equivalence

For expressions 3m + 4 and m + 4 + 2m:
- They are equivalent for m=1 and m=4.
To prove equivalence of 4(x + 3) + 2 and 6(x + 2):
- Evaluation at x=1 yields 18, and at x=8 the result is 60, confirming equivalence.

Evaluation Method

To determine if two expressions (e.g., 4x - x + 5 and 8 - 3x - 3) are equivalent:
- Use substitution and evaluate each expression with two different values.
- The expressions are equivalent if they yield the same results for both values substituted.

Properties of Expressions

The expression 7x + (5 + 6x) can be rewritten as (7x + 5) + 6x.
- This transformation demonstrates the use of the associative property, which allows grouping without changing the sum.
Incorrect application of the associative property can occur when crucial operators (like addition) are omitted in simplifications, as seen in Vance's transformation of (4.5m + 7/8) - 9 to 4.5m(7/8 - 9).

Explore the concept of equivalent expressions in algebra through various examples and simplifications. This quiz helps you understand how to determine equivalence and the simplification process of algebraic expressions. Test your knowledge on the properties of expressions and their evaluations.