Question

Louisa states that the solution to the equation 1/4x - 3 = 3/8x + 4 is x = 56. She verifies her solution using the steps below.

Equation: 1/4x - 3 = 3/8x + 4
Step 1: 1/4(56) - 3 = 3/8(56) + 4
Step 2: 14 - 3 = 21 + 4
Step 3: 11 = 25

Which statement most accurately describes Louisa’s error?

A. Louisa made an error when determining the original solution of x = 56.
B. Louisa made an error when substituting the solution in for x.
C. Louisa made an error when multiplying 56 by 1/4 and by 3/8
D. Louisa made an error when adding or subtracting.

Answer 1

option A

Explanation:

Given that Louisa states that the solution to the equation 1/4x - 3 = 3/8x + 4 is x = 56.

She did the following steps

Step 1 is right because she substituted x=14 to check whether right side = left side

Step 2: Multiplication is done correctly

Step 3: Is incorrect because 11 can never be equal to 25 in Mathematics.

Hence the mistake she did is not in substitution, multiplication or addition/subtraction. But in determining the original solution

Hence A) Louisa made an error when determining the original solution of x = 56.

Answer 2

A. Louisa made an error when determining the original solution of x = 56.

Explanation:

1/4x - 3 = 3/8x + 4

To verify x=56 is a solution, substitute x=56 into the equation

1/4(56) - 3 = 3/8(56) + 4

Multiply

14 -3 = 21 +4

Combine like terms

11 = 25

The steps are correct.

x=56 must not be a solution to the equation