Question

Answer 1

1)

a) \(2x-3>0\Leftrightarrow2x>3\Leftrightarrow x>\dfrac{3}{2}\)

b) \(5x-4< 4x+1\Leftrightarrow x< 5\)

c) \(\dfrac{2x-1}{2}-\dfrac{x+1}{6}\ge\dfrac{4x-5}{3}\)

\(\Leftrightarrow\dfrac{6x-3}{6}-\dfrac{x+1}{6}\ge\dfrac{8x-10}{6}\)

\(\Leftrightarrow6x-3-x-1\ge8x-10\Leftrightarrow-3x\ge-6\Leftrightarrow x\le2\)

2)

a) \(3a>3b\Leftrightarrow3a-5>3b-5\)

b) \(-4a< -4b\Leftrightarrow-4a+7< -4b+7\)

c) \(a^3>b^3,a^2b>ab^2\)

\(\Rightarrow a^3+a^2b>b^3+ab^2\)