Question

a parallelogram is shown below. judy was playing a game in class about quadrilaterals, and she came upon a problem she couldnt quite figure out. she needed this answer to unlock the clue to the next problem. in which step did judy make a mistake? ut = 6x - 22 and dt = x + 5. 2(x + 5)=6x - 22 step 1 x + 5 = 12x - 44 step 2 49 = 11x step 3 49/11 = x step 4 step 1 step 3 step 4 step 2

Explanation:

Step1: Analyze Step 1

In a parallelogram, the diagonals bisect each other. If $O$ is the mid - point of the diagonals, then $UT = 2DT$. So, $6x−22 = 2(x + 5)$ which is correct in Step 1.

Step2: Analyze Step 2

Starting from $6x−22 = 2(x + 5)$, when we distribute the 2 on the right - hand side, we get $6x−22=2x + 10$. If we try to simplify this to get to the form in Step 2 ($x + 5=12x−44$), it is incorrect. The correct way to simplify $6x−22 = 2x + 10$ is to subtract $2x$ from both sides and add 22 to both sides.

Step3: Analyze Step 3

Since Step 2 is wrong, any subsequent steps based on it are also wrong, but the error originated in Step 2.

Step4: Analyze Step 4

Same as Step 3, error started from Step 2.

Answer:

Step 2