During a deep-space mission, Emek and Tara noticed that two navigation software modules were producing different symbolic calculations for the spacecraft's next trajectory update. The expressions appeared different, but the team needed to know whether they represented the same mathematical value. Emek and Tara simplified both expressions by applying operation rules and combining like terms, then compared the equivalent results. Their analysis showed which program matched the correct navigation model and which contained an error. After selecting the consistent software module and updating the system, the spacecraft followed its planned path safely through space.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Combine the x terms and the constant terms in Module A before comparing.
Two navigation modules produced these expressions: Module A: 4x + 7 + 3x - 2 and Module B: 7x + 5. Are the two expressions equivalent?
Yes, because both simplify to 7x + 5Yes, because both simplify to 4x + 5No, because Module A simplifies to 7x + 9No, because variable terms cannot be combinedCorrect! Module A simplifies to the same expression as Module B.
Check the combination of like terms carefully before deciding if the expressions match.
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Hint
First apply multiplication to the parentheses, then substitute the value of x.
A navigation module uses the expression 3(x + 4) - 2x. If x = 5, what is the calculated trajectory value?
Correct! The expression gives 3(5 + 4) - 2(5) = 27 - 10 = 17.
Review the order of operations and evaluate the expression step by step.
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Hint
Distribute the 5 first, then combine the x terms.
Emek and Tara found two possible software expressions. Which expression is equivalent to 5(2x - 3) + x?
10x - 1511x - 1510x - 36x - 15Correct! Expanding gives 10x - 15 + x, which simplifies to 11x - 15.
Remember to include the extra x term after applying the distributive property.
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