الرياضيات المتناهية الأمثلة

\frac{2 (2 - 3 x)}{0.01} - 2.5 = \frac{0.02 - 2 x}{0.02} - 7.5

$\frac{2 (2 - 3 x)}{0.01} - 2.5 = \frac{0.02 - 2 x}{0.02} - 7.5$

خطوة 1

انقُل كل العبارات إلى المتعادل الأيسر.

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خطوة 1.1

اطرح

\frac{0.02 - 2 x}{0.02}

$\frac{0.02 - 2 x}{0.02}$ من كلا المتعادلين.

\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} = - 7.5

$\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} = - 7.5$

خطوة 1.2

أضف

7.5

$7.5$ إلى كلا المتعادلين.

\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0

$\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0

$\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

خطوة 2

بسّط

\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5

$\frac{2 (2 - 3 x)}{0.01} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5$ .

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خطوة 2.1

أوجِد القاسم المشترك.

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خطوة 2.1.1

اضرب

\frac{2 (2 - 3 x)}{0.01}

$\frac{2 (2 - 3 x)}{0.01}$ في

\frac{\frac{1}{0.01}}{\frac{1}{0.01}}

$\frac{\frac{1}{0.01}}{\frac{1}{0.01}}$ .

\frac{2 (2 - 3 x)}{0.01} \cdot \frac{\frac{1}{0.01}}{\frac{1}{0.01}} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0

$\frac{2 (2 - 3 x)}{0.01} \cdot \frac{\frac{1}{0.01}}{\frac{1}{0.01}} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

خطوة 2.1.2

اضرب

\frac{2 (2 - 3 x)}{0.01}

$\frac{2 (2 - 3 x)}{0.01}$ في

\frac{\frac{1}{0.01}}{\frac{1}{0.01}}

$\frac{\frac{1}{0.01}}{\frac{1}{0.01}}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} - 2.5 - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

خطوة 2.1.3

اكتب

- 2.5

$- 2.5$ على هيئة كسر قاسمه

1

$1$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

خطوة 2.1.4

اضرب

\frac{- 2.5}{1}

$\frac{- 2.5}{1}$ في

\frac{1}{1}

$\frac{1}{1}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} \cdot \frac{1}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} \cdot \frac{1}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

خطوة 2.1.5

اضرب

\frac{- 2.5}{1}

$\frac{- 2.5}{1}$ في

\frac{1}{1}

$\frac{1}{1}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{0.02 - 2 x}{0.02} + 7.5 = 0$

خطوة 2.1.6

اضرب

\frac{0.02 - 2 x}{0.02}

$\frac{0.02 - 2 x}{0.02}$ في

\frac{\frac{1}{0.02}}{\frac{1}{0.02}}

$\frac{\frac{1}{0.02}}{\frac{1}{0.02}}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - (\frac{0.02 - 2 x}{0.02} \cdot \frac{\frac{1}{0.02}}{\frac{1}{0.02}}) + 7.5 = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - (\frac{0.02 - 2 x}{0.02} \cdot \frac{\frac{1}{0.02}}{\frac{1}{0.02}}) + 7.5 = 0$

خطوة 2.1.7

اضرب

\frac{0.02 - 2 x}{0.02}

$\frac{0.02 - 2 x}{0.02}$ في

\frac{\frac{1}{0.02}}{\frac{1}{0.02}}

$\frac{\frac{1}{0.02}}{\frac{1}{0.02}}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + 7.5 = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + 7.5 = 0$

خطوة 2.1.8

اكتب

7.5

$7.5$ على هيئة كسر قاسمه

1

$1$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0$

خطوة 2.1.9

اضرب

\frac{7.5}{1}

$\frac{7.5}{1}$ في

\frac{1}{1}

$\frac{1}{1}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} \cdot \frac{1}{1} = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} \cdot \frac{1}{1} = 0$

خطوة 2.1.10

اضرب

\frac{7.5}{1}

$\frac{7.5}{1}$ في

\frac{1}{1}

$\frac{1}{1}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{0.01 (\frac{1}{0.01})} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0$

خطوة 2.1.11

اجمع

0.01

$0.01$ و

\frac{1}{0.01}

$\frac{1}{0.01}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{0.02 (\frac{1}{0.02})} + \frac{7.5}{1} = 0$

خطوة 2.1.12

اجمع

0.02

$0.02$ و

\frac{1}{0.02}

$\frac{1}{0.02}$ .

\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} + \frac{7.5}{1} = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} + \frac{7.5}{1} = 0$

\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} + \frac{7.5}{1} = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5}{1} - \frac{(0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} + \frac{7.5}{1} = 0$

خطوة 2.2

اجمع البسوط على القاسم المشترك.

\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5 + 7.5}{1} + \frac{- (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} = 0

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{- 2.5 + 7.5}{1} + \frac{- (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} = 0$

خطوة 2.3

أضف

$- 2.5$ و

$7.5$ .

$\frac{2 (2 - 3 x) \frac{1}{0.01}}{\frac{0.01}{0.01}} + \frac{5}{1} + \frac{- (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.02}{0.02}} = 0$

خطوة 2.4

اجمع البسوط على القاسم المشترك.

$\frac{2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.01}{0.01}} = 0$

خطوة 2.5

ألغِ العامل المشترك لـ

$0.01$ .

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خطوة 2.5.1

ألغِ العامل المشترك.

$\frac{2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02}}{\frac{0.01}{0.01}} = 0$

خطوة 2.5.2

أعِد كتابة العبارة.

$\frac{2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02}}{1} = 0$

خطوة 2.6

اقسِم

$2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02}$ على

$1$ .

$2 (2 - 3 x) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

خطوة 2.7

بسّط كل حد.

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خطوة 2.7.1

ألغِ العامل المشترك لـ

$0.01$ .

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خطوة 2.7.1.1

أخرِج العامل

$0.01$ من

$2 (2 - 3 x)$ .

$0.01 (200 (2 - 3 x)) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

خطوة 2.7.1.2

ألغِ العامل المشترك.

$0.01 (200 (2 - 3 x)) \frac{1}{0.01} + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

خطوة 2.7.1.3

أعِد كتابة العبارة.

$200 (2 - 3 x) + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

خطوة 2.7.2

طبّق خاصية التوزيع.

$200 \cdot 2 + 200 (- 3 x) + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

خطوة 2.7.3

اضرب

$200$ في

$2$ .

$400 + 200 (- 3 x) + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

خطوة 2.7.4

اضرب

$- 3$ في

$200$ .

$400 - 600 x + 5 - (0.02 - 2 x) \frac{1}{0.02} = 0$

خطوة 2.7.5

ألغِ العامل المشترك لـ

$0.02$ .

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خطوة 2.7.5.1

أخرِج العامل

$0.02$ من

$- (0.02 - 2 x)$ .

$400 - 600 x + 5 + 0.02 (- 50 (0.02 - 2 x)) \frac{1}{0.02} = 0$

خطوة 2.7.5.2

ألغِ العامل المشترك.

$400 - 600 x + 5 + 0.02 (- 50 (0.02 - 2 x)) \frac{1}{0.02} = 0$

خطوة 2.7.5.3

أعِد كتابة العبارة.

$400 - 600 x + 5 - 50 (0.02 - 2 x) = 0$

خطوة 2.7.6

طبّق خاصية التوزيع.

$400 - 600 x + 5 - 50 \cdot 0.02 - 50 (- 2 x) = 0$

خطوة 2.7.7

اضرب

$- 50$ في

$0.02$ .

$400 - 600 x + 5 - 1 - 50 (- 2 x) = 0$

خطوة 2.7.8

اضرب

$- 2$ في

$- 50$ .

$400 - 600 x + 5 - 1 + 100 x = 0$

خطوة 2.8

أضف

$400$ و

$5$ .

$- 600 x + 405 - 1 + 100 x = 0$

خطوة 2.9

أضف

$- 600 x$ و

$100 x$ .

$- 500 x + 405 - 1 = 0$

خطوة 2.10

اطرح

$1$ من

$405$ .

$- 500 x + 404 = 0$

خطوة 3

نطاق العبارة هو جميع الأعداد الحقيقية ما عدا ما يجعل العبارة غير معرّفة. في هذه الحالة، لا يوجد عدد حقيقي يجعل العبارة غير معرّفة.