Deep in an ancient mountain temple, Emek and Tara discovered a hidden passage protected by a series of symbolic gates. Each gate displayed a complex algebraic expression that had to be simplified before the lock would open. They carefully applied algebraic rules step by step, expanding, combining terms, and reorganizing the expressions until each final form matched the temple's required code. As they progressed deeper into the temple, the expressions became more challenging, but their calculations revealed the correct sequence. After unlocking the final gate, they discovered a lost explorer's journal containing valuable records of the ancient expedition.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Expand both parentheses before combining like terms.
A temple gate displays the expression 3(x + 4) - 2(x - 5). Which simplified form should Emek and Tara enter as the gate code?
x + 225x + 2x - 23x + 8Correct! Expanding gives 3x + 12 - 2x + 10, which simplifies to x + 22.
Check the signs when distributing the negative term through the second parentheses.
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Hint
Substitute x = 5 after expanding or evaluate each part carefully.
One temple lock uses the expression 4(2x - 3) - 3(x + 1). If x = 5, what integer value does the lock calculate?
Correct! The expression gives 4(10 - 3) - 3(6) = 28 - 18 = 10.
Review the substitution and the order of operations carefully.
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Hint
Use the distributive property by multiplying each term in the first parentheses by each term in the second.
A symbolic gate shows the expression (x + 3)(x - 2). Which expanded expression matches the gate code?
x^2 + x - 6x^2 - x - 6x^2 + 5x - 6x^2 - 6x + 6Correct! Multiplying gives x^2 - 2x + 3x - 6, which simplifies to x^2 + x - 6.
Check all four multiplication steps when expanding the two binomials.
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