Communication with several distant research probes suddenly stopped, and Emek and Tara hurried to the satellite control room. To realign the station's satellite array, they had to solve equations shown on different consoles. One screen displayed 5a - 8 = 27, while another showed 2(b + 4) = 22. Each correct value adjusted a different satellite panel, and the system checked every answer before allowing the next step. After completing all the calculations, the satellites locked into position, the communication link was restored, and the research mission continued successfully.
Challenges
Challenge 1 of 5
Challenges
Challenge 1 of 4
Hint
Substitute 5 into the equation, then solve for the actual value of a.
A technician claims that a = 5 solves the satellite equation 5a - 8 = 27. Which statement correctly checks the claim?
The claim is correct because 5(5) - 8 = 27.The claim is incorrect because a = 7.The claim is incorrect because a = 4.The claim is correct because 5 + 5 - 8 = 27.Correct! The claim fails, and solving the equation gives a = 7.
Check the proposed value by substitution and then solve the equation step by step.
Next🎉 Congrats! You got this question!
Hint
Divide both sides by 2 before subtracting 4.
The second satellite console displays 2(b + 4) = 22. What value of b correctly aligns the satellite panel?
Correct! The value of b is 7.
First isolate the quantity inside the parentheses, then solve for b.
Next🎉 Congrats! You got this question!
Hint
When distributing, multiply every term inside the parentheses.
Emek solves 2(b + 4) = 22 by writing 2b + 4 = 22. What mistake did he make?
He should have subtracted 2 from both sides first.He should have divided only b by 2.He did not distribute 2 to both terms inside the parentheses.He should have changed 22 to -22.Correct! The correct expansion is 2b + 8 = 22.
Check how the distributive property applies to both b and 4.
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🎉 Congrats! You finished this challenge set!
