Solve the inequality \((3-x)(5x+8)\geqslant9-3x\).

Solve the inequality \((x+2)(4 x-5) \leqslant 0\).

(a) Solve the inequality

\(3x^2-12x+16\gt 3x+4.\)

(b)(i) Write \(3x^2-12x+16\) in the form \(a(x+b)^2+c\), where \(a\), \(b\) and \(c\) are integers.

(b)(ii) Hence write down the equation of the tangent to the curve \(y=3x^2-12x+16\) at the minimum point of the curve.

Solve the inequality

\((2x+3)(x-4)\gt (3x+4)(x-1).\)

Solve the inequality

\((x+5)(x-2)\gt 3x+6.\)

Find the set of values of \(x\) for which

\(12x^2-20x+5 \lt (2x+1)(x-1).\)

Solve the inequality

\(|3x+2| \gt 8+x.\)

Solve the inequality

\((x-8)(x-10)\gt35.\)

(a) Find the values of \(x\) for which \((2x+1)^2\lt 3x+4\).

(b) Show that, whatever the value of \(k\), the equation \(\dfrac{x^2}{4}+kx+k^2+1=0\) has no real roots.

Find the values of \(x\) for which \(x(6x+7)\geq20\).

Find the values of \(x\) for which \(9x^2+18x-1\lt x+1\).

Solve the inequality

\((2-x)(x+9)\lt 10.\)

Solve the inequality

\((x-3)(x+4)\gt x+13.\)

Solve the inequality \((x-1)(x-5)\gt 12\).