AnswersMathematics 8Solving with Variables on Both Sides — QuizQuestion 5
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Solving with Variables on Both Sides — Quiz

Question 5 • Mathematics 8

Louisa states that the solution to the equation 1 fourth x minus 3 is equal to 3 eighths x plus 4 is x is equal to 56 She verifies her solution using the following steps. Louisa's Work Equation: 1 fourth x minus 3 is equal to 3 eighths x plus 4 Step 1: 1 fourth times 56 minus 3 is equal to 3 eighths times 56 plus 4 Step 2: 14 minus 3 is equal to 21 plus 4 Step 3: 11 is equal to 25 Which statement most accurately describes Louisa’s error?

Answer
A
Louisa made an error when substituting the solution in for x .
B
Louisa made an error when determining the original solution of x is equal to 56 .
C
Louisa made an error when multiplying 56 by 1 fourth and by 3 eighths .
D
Louisa made an error when adding or subtracting.

Explanation

Louisa substituted 56 correctly: one-fourth of 56 is 14, and three-eighths of 56 is 21, so her arithmetic gives 11 = 25. The equation is not true for x = 56, which means her original solution was incorrect. Solving the equation gives x = -56, so the correct choice is B, Louisa made an error when determining the original solution.

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