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Giải bài tập 2.15 trang 37 SGK Toán 9 tập 1 - Kết nối tri thức

Cho (a > b,) chứng minh rằng: a) (4a + 4 > 4b + 3;) b) (1 - 3a < 3 - 3b.)

Tổng hợp Đề thi vào 10 có đáp án và lời giải

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Đề bài

Cho \(a > b,\) chứng minh rằng: a) \(4a + 4 > 4b + 3;\) b) \(1 - 3a < 3 - 3b.\)

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng quy tắc: -  Cộng cả hai vế của bất đẳng thức với một số ta được bất đẳng thức cùng chiều với bất đẳng thức đã cho; -  Nhân cả hai vế của bất đẳng thức với cùng 1 số dương ta được một bất đẳng thức cùng chiều với bất đẳng thức đã cho; -  Nhân cả hai vế của bất đẳng thức với một số âm thì ta được một bất đẳng thức ngược chiều với bất đẳng thức đã cho. -  Áp dụng tính chất bắc cầu \(a < b;b < c\) thì \(a < c\)

Lời giải chi tiết

a) \(4a + 4 > 4b + 3;\) Ta có \(a > b\) nên \(4a > 4b\) (nhân cả hai vế với số dương 4) Suy ra \(4a + 3 > 4b + 3\) (cộng cả hai vế với số 3) Mà \(4a + 4 > 4a + 3\) nên \(4a + 4 > 4b + 3\) b) \(1 - 3a < 3 - 3b.\) Ta có \(a > b\) nên \( - 3a <  - 3b\) (nhân cả hai vế với số -3) Suy ra \(1 - 3a < 1 - 3b\) (cộng cả hai vế với 1) Mà \(1 - 3b < 3 - 3b\) nên \(1 - 3a < 3 - 3b.\)

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