Giải bất phương trình bậc nhất một ẩn là gì? Cách giải bất phương trình bậc nhất một ẩn - Toán 9

1. Khái niệm bất phương trình bậc nhất một ẩn

Bất phương trình dạng \(ax + b < 0\) (hoặc \(ax + b > 0\); \(ax + b \le 0\); \(ax + b \ge 0\)) trong đó a, b là hai số đã cho, \(a \ne 0\) được gọi là bất phương trình bậc nhất một ẩn x.

2. Khái niệm nghiệm của bất phương trình bậc nhất một ẩn

Số \({x_0}\) là một nghiệm của bất phương trình \(A\left( x \right) < B\left( x \right)\) nếu \(A\left( {{x_0}} \right) < B\left( {{x_0}} \right)\) là khẳng định đúng.

Tương tự đối với \(A\left( x \right) > B\left( x \right);A\left( x \right) \le B\left( x \right);A\left( x \right) \ge B\left( x \right)\).

3. Khái niệm giải bất phương trình

Giải một bất phương trình là tìm tất cả các nghiệm của bất phương trình đó.

4. Cách giải bất phương trình bậc nhất một ẩn

Bất phương trình bậc nhất một ẩn \(ax + b < 0\left( {a \ne 0} \right)\) được giải như sau:

\(\begin{array}{l}ax + b < 0\\ax < - b\end{array}\)

- Nếu \(a > 0\) thì \(x < \frac{{ - b}}{a}\).

- Nếu \(a < 0\) thì \(x > - \frac{b}{a}\).

Chú ý: ♔Các bất phương trình \(ax + b > 0\), \(ax + b \le 0\), \(ax + b \ge 0\) được giải tương tự.

Ta cũng có thể giải được các bất phương trình một ẩn đưa được về dạng \(ax + b < 0\), \(ax + b > 0\), \(ax + b \le 0\), \(ax + b \ge 0\).

5. Bài tập vận dụng

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