Solve for x: 3(x - 2) = 2(x + 1).

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Question: Solve for x: 3(x - 2) = 2(x + 1).

Options:

Correct Answer: 0

Solution:

Expanding both sides gives 3x - 6 = 2x + 2. Rearranging gives x = 8.

Solve for x: 3(x - 2) = 2(x + 1).

Solve for x: 3(x - 2) = 2(x + 1).

Correct Answer: 8

Step 1: Start with the equation 3(x - 2) = 2(x + 1).
Step 2: Distribute 3 on the left side: 3 * x - 3 * 2 = 3x - 6.
Step 3: Distribute 2 on the right side: 2 * x + 2 * 1 = 2x + 2.
Step 4: Now the equation looks like this: 3x - 6 = 2x + 2.
Step 5: To get all the x terms on one side, subtract 2x from both sides: 3x - 2x - 6 = 2.
Step 6: This simplifies to: x - 6 = 2.
Step 7: Now, add 6 to both sides to isolate x: x = 2 + 6.
Step 8: Finally, simplify to find x: x = 8.

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