\(a,4x-6< 7x-12\)

\(\Leftrightarrow6< 3x\Leftrightarrow x>2\)

\(b,\frac{3x-7}{4}\ge2-\frac{x+5}{3}\)

\(\Leftrightarrow3\left(3x-7\right)\ge24-4\left(x+5\right)\)

\(\Leftrightarrow13x\ge25\Leftrightarrow x\ge\frac{25}{13}\)

\(c,\frac{3x-8}{-7}\ge1-\frac{x+2}{-3}\)

\(\Leftrightarrow-3\left(3x-8\right)\ge21+7\left(x+2\right)\)

\(\Leftrightarrow-16x\ge11\)

\(\Leftrightarrow x\le-\frac{11}{16}\)

\(d,-12-8x>3+2x-\left(5-7x\right)\)

\(\Leftrightarrow14>17x\Leftrightarrow x< \frac{14}{17}\)

\(e,-1+\frac{x-1}{-3}\le\frac{x+2}{-9}\)

\(\Leftrightarrow-9-3\left(x-1\right)\le-\left(x+2\right)\)

\(\Leftrightarrow-2x\le4\Leftrightarrow x\ge-2\)

`Answer:`

\(3\left(1-x\right)+2=5-3x\)\(\Leftrightarrow3-3x+2=5-3x\)\(\Leftrightarrow5-3x=5-3x\)(đúng với mọi \(x\inℝ\))

Vậy phương trình đã cho có tập nghiệm \(S=ℝ\)

Áp dụng công thức \(\left(A+B+C\right):D=A:D+B:D+C:D\)

\(a,=\frac{1}{2}x^3y^3:xy^2+2x^2:xy^2+y^4:xy^2=\frac{x^2y}{2}+\frac{2x}{y^2}+\frac{y^2}{x}\)

\(b,=2x^4y:2x^2-6x^2y^7:2x^2+4x^5:2x^2=x^2y-3y^7+2x^3\)

\(c,=2x^2z^5:z^3-y^3z^3:z^3+4z^6:z^3=2x^2z^2-y^3+4z^3\)

\(d,=2\left(x-2y\right)^4:\left(x-2y\right)-9\left(x-2y\right)^3:\left(x-2y\right)+2\left(x-2y\right):\left(x-2y\right)=2\left(x-2y\right)^3-9\left(x-2y\right)^2+2\)