Podcast
Questions and Answers
Which statements about the expressions 5 + 3x - 2 and x + 2(x + 1) + 1 are true? (Select all that apply)
Which statements about the expressions 5 + 3x - 2 and x + 2(x + 1) + 1 are true? (Select all that apply)
Which statements about the expressions 7x + 4 and 3x + 5 + 4x - 1 are true? (Select all that apply)
Which statements about the expressions 7x + 4 and 3x + 5 + 4x - 1 are true? (Select all that apply)
Which expression is equivalent to 7(xy)?
Which expression is equivalent to 7(xy)?
Which expressions are equivalent to 8.9x + 6.2 + 8.7? (Select all that apply)
Which expressions are equivalent to 8.9x + 6.2 + 8.7? (Select all that apply)
Which expressions are equivalent when m = 1 and m = 4?
Which expressions are equivalent when m = 1 and m = 4?
What proves why the expressions 4(x + 3) + 2 and 6(x + 2) are equivalent?
What proves why the expressions 4(x + 3) + 2 and 6(x + 2) are equivalent?
Which method determines if the expressions 4x - x + 5 and 8 - 3x - 3 are equivalent using substitution?
Which method determines if the expressions 4x - x + 5 and 8 - 3x - 3 are equivalent using substitution?
Which expressions are equivalent to g + h + (j + k)? (Select all that apply)
Which expressions are equivalent to g + h + (j + k)? (Select all that apply)
Did Vance apply the associative property correctly when writing (4.5m + 7/8) - 9 as the equivalent expression 4.5m(7/8 - 9)?
Did Vance apply the associative property correctly when writing (4.5m + 7/8) - 9 as the equivalent expression 4.5m(7/8 - 9)?
Which property was applied to create the equivalent expression 7x + (5 + 6x) -----> (7x + 5) + 6x?
Which property was applied to create the equivalent expression 7x + (5 + 6x) -----> (7x + 5) + 6x?
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Study Notes
Equivalent Expressions Overview
- Equivalent expressions yield the same value for all values of the variable.
- To determine equivalence, substitute values into the expressions.
Card 1 Insights
- Expressions: 5 + 3x - 2 and x + 2(x + 1) + 1 evaluated at x = 3 and x = 7.
- Both expressions equal x + 6.
- They are equivalent for any value of x, confirmed with x = 10 yielding a value of 33.
Card 2 Insights
- Expressions: 7x + 4 and 3x + 5 + 4x - 1 evaluated at x = 4 and x = 6.
- For x = 2, both expressions give a value of 18.
- They are equivalent for all x, also verified for x = 8.
Card 3 Insight
- Expression equivalent to 7(xy) is x(7y), illustrating distributive property.
Card 4 Insights
- Expressions: 8.9x + 6.2 + 8.7 can be rearranged as:
- 8.9x + 8 - 7 + 6.2
- 8.7 + 8.9x + 6.2
- 6.2 + 8.7 + 8.9x
Card 5 Insight
- Expression equivalence for m = 1 and m = 4: 3m + 4 and m + 4 + 2m.
Card 6 Insight
- Expressions: 4(x + 3) + 2 and 6(x + 2) examined at x = 1 (value 18) and x = 8 (value 60).
- Values match, confirming equivalence.
Card 7 Insight
- Correct method involves evaluating both expressions with two different values.
- If results are identical for both substitutions, expressions are equivalent.
Card 8 Insights
- Expressions equivalent to g + h + (j + k):
- g + (h + j) + k
- (g + h) + j + k
Card 9 Insight
- Vance incorrectly applied the associative property.
- The addition symbol was omitted in the transformation (4.5m + 7/8) - 9 to 4.5m(7/8 - 9).
Card 10 Insight
- The property used was the associative property to rearrange 7x + (5 + 6x) to (7x + 5) + 6x.
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