During a mountain expedition, Emek and Tara depended on a navigation console to guide their team through unfamiliar terrain. After a powerful storm damaged the system, the route commands were replaced with complicated symbolic expressions. The console could only restore the original directions if the expressions were simplified correctly. Emek and Tara analyzed each expression, applying algebraic rules such as distributing terms, combining like terms, and simplifying the results step by step. By comparing the simplified forms with the stored route patterns, they identified the correct commands. The repaired console revealed a safe path through the mountains, allowing the expedition team to continue their journey successfully.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Distribute each coefficient first, then combine like terms.
The navigation console displays the route command expression 2(3x - 4) + 5(x + 2). Which simplified form should Emek and Tara use?
11x + 211x - 86x + 1015x + 6Correct! Expanding gives 6x - 8 + 5x + 10, which simplifies to 11x + 2.
Check the distribution step and the signs of the constant terms.
Next🎉 Congrats! You got this question!
Hint
Substitute x = 6 and follow the order of operations carefully.
A route command is represented by the expression 3(2x - 5) - 2(x + 4). If x = 6, what integer value does the console calculate?
Correct! The expression evaluates to 1.
Review the substitution and multiplication steps before combining the results.
Next🎉 Congrats! You got this question!
Hint
Multiply every term in the first binomial by every term in the second binomial.
The console compares two stored route patterns. Which expression is equivalent to (x + 4)(x - 3)?
x^2 + x - 12x^2 - x - 12x^2 + 7x - 12x^2 - 12x + 1Correct! Expanding gives x^2 - 3x + 4x - 12, which simplifies to x^2 + x - 12.
Check the middle terms carefully when multiplying the binomials.
Next🎉🎉🎉🎉🎉🎉🎉🎉
🎉 Congrats! You finished this challenge set!
