Aboard a space station, Emek and Tara discovered that the navigation system had lost power. To restart it safely, they needed to enter the exact energy level required by the Expression Engine. The screen displayed 4m + 7 + 3m - 2, where m represented the number of active navigation modules. Instead of substituting immediately, Tara combined the like terms. The expression simplified to 7m + 5. Emek checked the control panel and found that 6 modules were active. Substituting 6 for m gave 7(6) + 5, so the system required 47 energy units. They entered 47 and watched the navigation display glow to life. By simplifying first and then evaluating the expression, Emek and Tara restored the system without wasting energy, and the station returned safely to its planned course.

Challenges

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Challenge 1 of 5

Challenges

Start
Challenge 1 of 4
Hint
Combine the terms containing m, and then combine the constant terms.
The Expression Engine displays 4m + 7 + 3m - 2. Which expression is equivalent to it?
7m + 912m + 57m + 57m - 5
Correct. The like terms combine to give 7m + 5.
Combine 4m with 3m and combine 7 with -2 separately.
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Hint
Substitute 8 for m in 7m + 5 and evaluate.
Later, the Expression Engine still uses the simplified rule 7m + 5, but the control panel shows 8 active navigation modules. How many energy units are required?
Correct. With 8 active modules, the engine requires 61 energy units.
Replace m with 8, multiply 7 by 8, and then add 5.
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Hint
Every m in the original expression should be replaced by 6.
Emek wants to check the 47-energy-unit result without using the simplified expression. Which calculation correctly substitutes 6 directly into the original expression 4m + 7 + 3m - 2?
4 + 6 + 7 + 3 + 6 - 24(6) + 7 + 3(6) - 24(6 + 7) + 3(6 - 2)4(6) + 7 + 3 - 6 - 2
Correct. Substituting 6 for both occurrences of m gives 4(6) + 7 + 3(6) - 2.
Replace each occurrence of m with 6 while keeping all operations in the original expression unchanged.
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İfade Motoruna Güç Vermek
TR
ARC_G07_PA_02_STORY_01
İfade Motoruna Güç Vermek
Powering the Expression Engine
EN
ARC_G07_PA_02_STORY_01
Powering the Expression Engine