Question
\( \frac{3}{}(2x-\frac{x}{2})=\frac{x+1}{3} \)
Ask by Reeves Bryant. in Turkey
Jan 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = \frac{2}{25} \)
Solution
لحل المعادلة:
\[
3\left(2x - \frac{x}{2}\right) = \frac{x + 1}{3}
\]
**الخطوات:**
1. **تبسيط الطرف الأيسر:**
\[
3\left(2x - \frac{x}{2}\right) = 3\left(\frac{4x}{2} - \frac{x}{2}\right) = 3\left(\frac{3x}{2}\right) = \frac{9x}{2}
\]
2. **المعادلة بعد التبسيط:**
\[
\frac{9x}{2} = \frac{x + 1}{3}
\]
3. **التخلص من المقامات بضرب الطرفين في 6:**
\[
6 \times \frac{9x}{2} = 6 \times \frac{x + 1}{3} \\
27x = 2(x + 1)
\]
4. **توزيع وإيجاد قيمة \(x\):**
\[
27x = 2x + 2 \\
27x - 2x = 2 \\
25x = 2 \\
x = \frac{2}{25}
\]
**إذاً، حل المعادلة هو:**
\[
x = \frac{2}{25}
\]
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Simplify this solution Mind Expander
To solve the equation \( \frac{3}{}(2x-\frac{x}{2})=\frac{x+1}{3} \), let's first simplify the left-hand side. We combine the terms inside the parentheses: \[ 2x - \frac{x}{2} = \frac{4x}{2} - \frac{x}{2} = \frac{3x}{2} \] Now the equation looks like: \[ 3 \cdot \frac{3x}{2} = \frac{x+1}{3} \] This simplifies to: \[ \frac{9x}{2} = \frac{x+1}{3} \] Next, we cross-multiply to eliminate the fractions: \[ 9x \cdot 3 = (x + 1) \cdot 2 \] This expands to: \[ 27x = 2x + 2 \] To isolate \(x\), subtract \(2x\) from both sides: \[ 27x - 2x = 2 \] \[ 25x = 2 \] Now divide both sides by 25: \[ x = \frac{2}{25} \] So the solution to the equation is: \[ x = \frac{2}{25} \]
