$$ \frac { 20 } { } \frac { x - 700 } { 3 - 7 } = ( - 1 - 2 ) \cdot 20 $$

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UpStudy AI · Accepted Answer

Solve the equation by following steps:
- step0: Solve for $$x$$:
  $$\frac{20}{\frac{x-700}{3-7}}=\left(-1-2\right)\times 20$$
- step1: Find the domain:
  $$\frac{20}{\frac{x-700}{3-7}}=\left(-1-2\right)\times 20,x\neq 700$$
- step2: Simplify:
  $$-\frac{80}{x-700}=-60$$
- step3: Rewrite the expression:
  $$\frac{-80}{x-700}=-60$$
- step4: Cross multiply:
  $$-80=\left(x-700\right)\left(-60\right)$$
- step5: Simplify the equation:
  $$-80=-60\left(x-700\right)$$
- step6: Rewrite the expression:
  $$-20\times 4=-20\times 3\left(x-700\right)$$
- step7: Evaluate:
  $$4=3\left(x-700\right)$$
- step8: Swap the sides:
  $$3\left(x-700\right)=4$$
- step9: Divide both sides:
  $$\frac{3\left(x-700\right)}{3}=\frac{4}{3}$$
- step10: Divide the numbers:
  $$x-700=\frac{4}{3}$$
- step11: Move the constant to the right side:
  $$x=\frac{4}{3}+700$$
- step12: Add the numbers:
  $$x=\frac{2104}{3}$$
- step13: Check if the solution is in the defined range:
  $$x=\frac{2104}{3},x\neq 700$$
- step14: Find the intersection:
  $$x=\frac{2104}{3}$$
لحل المعادلة المعطاة:

$$
\frac{20}{\frac{x - 700}{3 - 7}} = (-1 - 2) \cdot 20
$$

نبدأ بتبسيط الجانبين:

1. **تبسيط الجانب الأيمن**:
   $$
   (-1 - 2) \cdot 20 = -3 \cdot 20 = -60
   $$

2. **إعادة كتابة المعادلة**:
   $$
   \frac{20}{\frac{x - 700}{3 - 7}} = -60
   $$

3. **تبسيط المقام**:
   $$
   3 - 7 = -4
   $$
   لذا تصبح المعادلة:
   $$
   \frac{20}{\frac{x - 700}{-4}} = -60
   $$

4. **إعادة كتابة المعادلة**:
   $$
   \frac{20 \cdot (-4)}{x - 700} = -60
   $$

5. **تبسيط المعادلة**:
   $$
   \frac{-80}{x - 700} = -60
   $$

6. **إزالة السالب من الجانبين**:
   $$
   \frac{80}{x - 700} = 60
   $$

7. **ضرب كلا الجانبين في $$x - 700$$**:
   $$
   80 = 60(x - 700)
   $$

8. **توسيع المعادلة**:
   $$
   80 = 60x - 42000
   $$

9. **إضافة 42000 لكلا الجانبين**:
   $$
   60x = 80 + 42000
   $$
   $$
   60x = 42080
   $$

10. **قسمة كلا الجانبين على 60**:
    $$
    x = \frac{42080}{60}
    $$
    $$
    x = 701.33
    $$

وبذلك، الحل النهائي هو:
$$
x = \frac{2104}{3} \quad \text{أو} \quad x = 701.33
$$
$$ x = \frac{2104}{3} $$ أو $$ x = 701.33 $$

\( \frac { 20 } { } \frac { x - 700 } { 3 - 7 } = ( - 1 - 2 ) \cdot 20 \)

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