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題目

解題步驟

1. Understand the question

   Turn 1 Question

   1. solve for x in simplest form.

   $9 = \\frac{1}{2}(9x + 6)$

   Turn 2 Question

   Send a few similar problems

   Turn 3 Question

   1.x=9

   Turn 4 Question

   Yes

   Turn 5 Question

   I’ll do B

   Turn 6 Question

   The answer is x=3.5

   Turn 7 Question

   I’ll try a third one

   Turn 8 Question

   The answer is 2

   Turn 9 Question

   I’ll call it a day

2. Response

   Turn 1 Answer

3. Explanation

   Step1: Multiply both sides by 2

   To eliminate the fraction, multiply each side of the equation \( 9 = \frac{1}{2}(9x + 6) \) by 2.
   \[
   2\times9 = 2\times\frac{1}{2}(9x + 6)
   \]
   Simplifying both sides gives:
   \[
   18 = 9x + 6
   \]

   Step2: Subtract 6 from both sides

   Subtract 6 from each side of the equation \( 18 = 9x + 6 \) to isolate the term with \( x \).
   \[
   18 - 6 = 9x + 6 - 6
   \]
   Simplifying both sides gives:
   \[
   12 = 9x
   \]

   Step3: Divide both sides by 9

   Divide each side of the equation \( 12 = 9x \) by 9 to solve for \( x \).
   \[
   x = \frac{12}{9}
   \]
   Simplify the fraction \( \frac{12}{9} \) by dividing the numerator and denominator by their greatest common divisor, which is 3.
   \[
   x = \frac{4}{3}
   \]

4. Final answer

   \( x = \frac{4}{3} \)

   Turn 2 Answer

   Knowledge Points:

   • Solving linear equations with one variable.
   • Using inverse operations (multiplication, subtraction, division) to isolate the variable.
   • Simplifying fractions by dividing numerator and denominator by their greatest common divisor.
   • Distributive property (when applying inverse operations to eliminate parentheses).
   • Combining like terms during the process of solving the equation.

   Quiz problems:

   1. Solve for \( x \) in simplest form: \( 8=\frac{1}{3}(6x + 9) \)
   2. Solve for \( x \) in simplest form: \( 10=\frac{1}{4}(8x + 12) \)
   3. Solve for \( x \) in simplest form: \( 7=\frac{1}{5}(10x + 15) \)

   Turn 3 Answer

   Nice job getting that first one! Let me check—wait, hold on, let's walk through it quick to make sure. Starting with 8 = 1/3(6x + 9), multiply both sides by 3 first: 24 = 6x + 9. Then subtract 9: 15 = 6x. Divide by 6, and simplify 15/6 to 5/2 (or 2.5). Oops, looks like you might have made a tiny misstep! No worries though, algebra can be tricky. Wanna try again or move to the next one?

   Turn 4 Answer

   Alright, let's give that first one another go, or jump straight to problem 2—your call! 😊

   A. Retry problem 1: \( 8=\frac{1}{3}(6x + 9) \)
   B. Move to problem 2: \( 10=\frac{1}{4}(8x + 12) \)

   Turn 5 Answer

   Awesome, let's tackle problem 2: \( 10=\frac{1}{4}(8x + 12) \)

   Take it step by step—you got this!

   Turn 6 Answer

   Perfect! That's exactly right (and if we want to write it as a fraction, it's 7/2, but 3.5 works too). Great job breaking it down 😎 Wanna try the third one now, or take a quick break?

   Turn 7 Answer

   Let's go for it! Problem 3 is: \( 7=\frac{1}{5}(10x + 15) \)

   You've been crushing these, I know you've got this!

   Turn 8 Answer

   YES, that's 100% correct! 🎉 You totally nailed all these—great work with the fractions and isolating x. Wanna do a couple more for extra practice, or call it a win for today?

   Turn 9 Answer

   Smart move—you earned that break! 🎊 Great job working through those equations today, you’re really getting the hang of this. Catch you next time!

答案

Question Analysis

OCR Text

I’ll call it a day

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