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QuizMultiple Choice

Solving Linear Equations: Variables on Both Sides — Quiz

Question 3 • *KCPS Algebra I (2027)

Use properties to rewrite the given equation. Which equations have the same solution as the equation? 3 fifths x plus 2 thirds plus x is equal to 1 half minus 1 fifth x Choose three correct answers.

Answer
A
8 fifths x plus 2 thirds is equal to 1 half minus 1 fifth x
B
18 x plus 20 plus x is equal to 15 minus 6 x
C
24 x plus 30 x is equal to negative 5
D
18 x plus 20 plus 30 x is equal to 15 minus 6 x
E
12 x plus 30 x is equal to negative 5

Explanation

Combine the x-terms on the left: 3/5x + x = 8/5x, giving choice A. Multiplying the original equation by 30 gives 18x + 20 + 30x = 15 − 6x, which is choice D. Simplifying that equation gives 54x = −5, matching choice C. Choice E has 42x on the left, so it does not have the same solution.

AI-written and checked against the verified answer.

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