Deep inside an ancient temple, Emek and Tara uncovered a faded map whose directions were hidden in algebraic expressions instead of ordinary words. To move from one chamber to the next, they simplified each expression by combining like terms. One clue changed 7a - 4 + 5a + 9 into 12a + 5, while another became 9b - 6 after simplifying 4b + 8 - 3 + 5b - 11. Each simplified result revealed the correct passage through the maze. By carefully interpreting every clue, they reached the final chamber and recovered the long-lost historical artifact.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Combine the x-terms and the constant terms separately.
A temple clue shows 6x + 7 - 2x - 3. Which simplified expression reveals the correct passage?
4x + 108x + 44x + 46x + 2Correct! 6x - 2x = 4x and 7 - 3 = 4.
Group the like terms before simplifying.
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Hint
Simplify the variable terms and constants first, then subtract b from a.
Another map clue is 11y - 8 + 3y + 5. After simplifying it to ay + b, what is the value of a - b?
Correct! The expression is 14y - 3, so 14 - (-3) = 17.
Identify both a and b carefully, including the sign of b.
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Hint
Simplify each expression separately and compare the results.
Two passages are labeled with the expressions 3m + 6 + 4m - 2 and 9m + 1 - 2m + 3. Which statement is true?
The expressions are equivalent because both simplify to 7m + 4.The first simplifies to 7m + 8, and the second simplifies to 7m + 4.The expressions are not equivalent because their original terms appear in a different order.The first simplifies to 12m + 4, and the second simplifies to 11m + 4.Correct! Both expressions simplify to 7m + 4.
Combine like terms in each expression before deciding whether they are equivalent.
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