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ماشین‌حساب معادلهٔ خطی

این ماشین‌حساب معادله‌هایی به شکل ax + b = c را حل می‌کند. a، b و c را وارد کنید تا Sumzo متغیر x را گام‌به‌گام تنها کند، کسرها را دقیق نگه دارد و پاسخ را بررسی کند.

عدد صحیح، اعشاری یا کسرهایی مثل 3/4

نتیجه

مقادیر را وارد کنید و برای دیدن نتیجه «محاسبه» را بزنید.

فرمول

ax+b=c  ⇒  x=c−baax + b = c \;\Rightarrow\; x = \frac{c - b}{a}

Subtract b from both sides, then divide by a (when a ≠ 0).

نحوه استفاده از این ماشین‌حساب

  1. Rearrange your equation into the form ax + b = c (e.g. 5 − 2x = 9 has a = −2, b = 5, c = 9).
  2. Enter a, b and c and press Calculate.

مثال‌های حل‌شده

Solve 3x + 5 = 20

Subtract 5 from both sides: 3x = 15.

Divide by 3: x = 5. Check: 3 · 5 + 5 = 20.

Medium: a fraction in front of x

For (2/3)x − 1 = 5, enter a = 2/3, b = −1 and c = 5.

Add 1 to both sides: (2/3)x = 6.

Divide by 2/3, which is the same as multiplying by 3/2: x = 6 × 3/2 = 9.

Check: (2/3) × 9 − 1 = 6 − 1 = 5 ✓.

Hard: decimals and a negative answer

For 0.4x + 1.2 = −2, enter a = 0.4, b = 1.2 and c = −2.

Subtract 1.2 from both sides: 0.4x = −3.2.

Divide by 0.4: x = −8.

Check: 0.4 × (−8) + 1.2 = −3.2 + 1.2 = −2 ✓.

اشتباه‌های رایج

  • Moving a term without changing its sign: from 3x + 5 = 20, subtracting 5 gives 3x = 15, not 3x = 25.
  • Dividing by the wrong number: in 0.4x = −3.2 divide by 0.4, giving −8, not −0.8.
  • Forgetting to rearrange into ax + b = c first: 5 − 2x = 9 has a = −2, b = 5 and c = 9.

پرسش‌های متداول

How do I solve linear equations with x on both sides?

Collect the x terms on one side first: 5x − 3 = 2x + 9 becomes 3x − 3 = 9, which is ax + b = c with a = 3, b = −3 and c = 9 (so x = 4).

What if a = 0?

Then there is no x term. If b = c every number is a solution; otherwise there is no solution. Sumzo tells you which.

Can I solve equations with x on both sides?

Collect the x terms on one side first, or type the whole equation into Sumzo AI, which handles that automatically.

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