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Question Find Sharon's mistake in solving the equation 9=−3(e−2)9=-3(e-2) step-by-step.

Studdy Solution

STEP 1

Assumptions
1. Sharon is solving the equation step by step.
2. The original equation is 9=−3(e−2)9=-3(e-2).
3. We need to check each step for any mistakes.

STEP 2

Let's verify Step 1 of Sharon's solution. She distributed the −3-3 to both ee and −2-2.
9=−3(e−2)9=-3(e-2)
9=−3e+69=-3e+6
This step is correct.

STEP 3

Now, let's verify Step 2. Sharon added 66 to both sides of the equation to isolate the term with ee.
9=−3e+69=-3e+6
9−6=−3e+6−69-6=-3e+6-6
3=−3e3=-3e
Sharon made a mistake here. She should have subtracted 66 from 99, which gives 33, not 1515.

STEP 4

Correcting Sharon's mistake in Step 2, we should have:
3=−3e3=-3e
Now, we need to solve for ee.

STEP 5

To find the value of ee, we divide both sides of the equation by −3-3.
3−3=−3e−3\frac{3}{-3} = \frac{-3e}{-3}

STEP 6

Solve for ee.
e=−1e = -1
Sharon's mistake was in Step 2 where she incorrectly added 66 to 99 instead of subtracting it. The correct solution is e=−1e = -1.

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