Question

1. Cho a < b, chứng tỏ rằng:

a). \(3-6a>1-6b\)

b). \(7\left(a-2\right)< 7\left(b-2\right)\)

c). \(\dfrac{1-2a}{3}>\dfrac{1-2b}{3}\)

2. So sánh a và b nếu:

a). \(a+23< b+23\)

b). \(-12a>-12b\)

c). \(5a-6\ge5b-6\)

d). \(\dfrac{-2a+3}{5}\le\dfrac{-2b+3}{5}\)

Answer 1

Bài 1:

a). Ta có: a < b

=> -6a > -6b

mà 3 > 1

=> \(3-6a>1-6b\)

b)

Ta có: a < b

=> a - 2 < b - 2

=> \(7\left(a-2\right)< 7\left(b-2\right)\)

c)

Ta có: a < b

=> -2a > -2b

=> 1 - 2a > 1 - 2b

\(\Rightarrow\dfrac{1-2a}{3}>\dfrac{1-2b}{3}\)

Answer 2

Bài 2:

a) Ta có:

a+23<b+23

\(\Leftrightarrow a< b\)

b) Ta có:

\(-12a>-12b\)

\(\Leftrightarrow a< b\)

c) Ta có:

\(5a-6\ge5b-6\)

\(a\ge b\)

d) Ta có:

\(\dfrac{-2a+3}{5}\le\dfrac{-2b+3}{5}\)

\(\Leftrightarrow-2a+3\le-2b+3\)

\(\Leftrightarrow a\ge b\)