As a powerful storm approached, Emek and Tara climbed to a mountain summit to repair an emergency beacon before darkness fell. The beacon's control panels displayed algebraic expressions that had to be simplified in the correct order to restore power. They first simplified 6m + 9 - 2m - 5 to 4m + 4, then simplified 3n - 7 + 8n + 2 to 11n - 5. Each correct result activated another section of the system. When the final panel powered on, the beacon illuminated the mountain, guiding nearby explorers safely through the storm.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Check the variable terms and the constant terms separately.
A beacon panel shows 8x - 6 + 3x + 4. Tara says it simplifies to 11x - 10. Which statement correctly checks her work?
Tara is incorrect because the expression simplifies to 11x - 2.Tara is correct because -6 + 4 = -10.Tara is incorrect because the expression simplifies to 5x - 2.Tara is correct because 8x + 3x = 11x.Correct! The x-terms make 11x, while -6 + 4 equals -2.
Recalculate the constants carefully and then compare the full expressions.
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Hint
Combine the y-terms and constants first, including the sign of each term.
Another control panel shows 12y - 9 - 5y + 3. After simplifying the expression to ay + b, what is the value of a + b?
Correct! The expression becomes 7y - 6, and 7 + (-6) = 1.
Simplify the expression first, then add the signed values of a and b.
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Hint
Substitute 2 for n in both expressions and evaluate each one.
Emek checks the panel result 3n - 7 + 8n + 2 = 11n - 5 by substituting n = 2. Which comparison verifies that the two expressions are equivalent?
The original expression has a value of 11, but 11n - 5 has a value of 17.The original expression has a value of 17, but 11n - 5 has a value of 27.Both expressions have a value of 22.Both expressions have a value of 17.Correct! Both expressions equal 17 when n = 2.
Evaluate the original and simplified expressions separately using n = 2.
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