Question

Celia uses the steps below to solve the equation Negative StartFraction 3 over 8 EndFraction (negative 8 minus 16 d) + 2 d = 24. Step 1 Distribute Negative StartFraction 3 over 8 EndFraction over the expression in parentheses. 3 minus 16 d + 2 d = 24 Step 2 Simplify like terms. 3 minus 14 d = 24 Step 3 Subtract 3 from both sides of the equation. Negative 14 d = 21 Step 4 Divide both sides of the equation by –14. D = StartFraction 21 over negative 14 EndFraction = Negative three-halves = negative 1 and one-half Which corrects the error in the step in which Celia made the first error?

Answer 1

Celia's first error was in distributing the negative fraction -3/8 over the expression in parentheses. The correct equation after distributing should be 3 + 16d + 2d = 24. After correcting this error, the rest of Celia's steps are correct, and the solution is d = -1.5.

Step-by-step explanation:

The error in Celia's first step is in the distribution of the negative fraction -3/8 over the expression in parentheses. The correct distribution should result in -3 + 16d + 2d = 24. This is because multiplying a negative fraction by a negative number results in a positive value. So, the correct equation after distributing is 3 + 16d + 2d = 24.

After correcting this error, the rest of Celia's steps are correct. Simplifying like terms, we have 18d + 3 = 24. Subtracting 3 from both sides gives us 18d = 21. Finally, dividing both sides by -18, we find that d = -21/18 = -3/2 = -1.5.

Answer 2

The answer is B

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