While crossing a remote canyon, Emek and Tara discovered a series of ancient stone gates blocking the trail to a hidden valley. Each gate displayed an algebraic expression that had to be simplified before it would open. At the first gate, they combined like terms to simplify 5x + 3 - 2x + 4 into 3x + 7. At the next gate, they rewrote 8y - 5 + 2 - 3y as 5y - 3. Each correct simplification unlocked another passage. By carefully combining like terms at every checkpoint, they opened the final gate and reached the hidden valley before sunset.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Combine the x-terms together and the constants together.
At another canyon gate, Emek sees the expression 7x + 6 - 3x + 2. Which simplified expression will open the gate?
4x + 810x + 84x + 47x + 5Correct! 7x - 3x = 4x and 6 + 2 = 8.
Group like terms before simplifying.
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Hint
First combine the y-terms and constants, then add the two resulting coefficients.
A stone gate shows 9y - 4 + 5 - 2y. After simplifying the expression to ay + b, what is the value of a + b?
Correct! The simplified expression is 7y + 1, and 7 + 1 = 8.
Simplify the expression first, then identify a and b.
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Hint
Check the variable terms and constant terms separately.
Tara simplifies 12m - 7 + 3m - 5 as 15m - 12. Which statement correctly checks her work?
Her work is correct because 12m + 3m = 15m and -7 - 5 = -12.Her work is incorrect because the answer should be 9m - 2.Her work is incorrect because m-terms and constants should be combined together.Her work is correct because 12 + 3 - 7 - 5 = 15.Correct! Tara combined each pair of like terms accurately.
Verify the m-terms and constants in separate groups.
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