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Giải và tính giá trị tuyệt đối

Công cụ này giải các phương trình như |2x − 3| = 7 bằng cách chia thành hai trường hợp, kiểm tra từng đáp án và báo cho bạn khi vô nghiệm. Nó cũng tìm giá trị tuyệt đối của một số, ví dụ |−7.5| = 7.5.

Kết quả

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Công thức

∣u∣=c  (c>0)  ⟺  u=c or u=−c\lvert u \rvert = c \;(c > 0) \iff u = c \text{ or } u = -c

Split the equation into two cases. If c = 0 there is one case; if c < 0 there is no solution.

∣x∣={xx≥0−xx<0\lvert x \rvert = \begin{cases} x & x \geq 0 \\ -x & x < 0 \end{cases}

The absolute value is the distance from 0, so it is never negative.

Cách dùng máy tính này

  1. To solve an equation, choose “Solve |ax + b| = c” and enter a, b and c — for |2x − 3| = 7 that is 2, −3 and 7.
  2. To find the absolute value of a number, choose the second option and enter the number: drop its minus sign, if it has one.
  3. Press Calculate to see both cases, the solutions and the check.

Ví dụ giải mẫu

Solve |2x − 3| = 7

Case 1: 2x − 3 = 7, so x = 5. Case 2: 2x − 3 = −7, so x = −2.

Check: |2·5 − 3| = 7 and |2·(−2) − 3| = |−7| = 7.

One solution: |x + 4| = 0

Only 0 has absolute value 0, so x + 4 = 0 and x = −4.

No solution: |3x − 1| = −2

An absolute value is never negative, so it can’t equal −2: no solution.

The absolute value of −7.5

−7.5 is 7.5 units from 0, so |−7.5| = 7.5.

Lỗi thường gặp

  • Solving only the positive case: |u| = 7 also gives u = −7.
  • Solving |u| = −2 anyway — an absolute value can’t be negative.
  • Distributing the bars: |a − b| is not |a| − |b|.
  • Forgetting to check answers, which matters when x appears outside the bars too.

Câu hỏi thường gặp

How do you find the absolute value of a number?

Take its distance from 0: remove the minus sign if there is one. |−12| = 12 and |5| = 5.

How do you solve an absolute value equation?

Get the absolute value on its own, then split into two equations: the inside equals c, or the inside equals −c. Solve both and check.

When does an absolute value equation have no solution?

When the absolute value is set equal to a negative number, such as |3x − 1| = −2.

What about absolute value inequalities?

Use the inequality calculator: it solves |2x − 1| ≥ 5 and similar, and draws the solution on a number line.