Solve quadratic inequality

Find the set of values of \(x\) for which $$(x - 1)(x - 2) < 20.$$ [4]

Determine the set of values of \(x\) which satisfy the inequality $$3x^2 + 3x > x + 6$$ Give your answer in exact form using set notation. [4 marks]

Consider the two statements, A and B, below. A: \(x^2 - 6x + 8 > 0\) B: \(x > 4\) Choose the most appropriate option below. Circle your answer. [1 mark] \(A \Rightarrow B\) \(A \Leftarrow B\) \(A \Leftrightarrow B\) There is no connection between A and B

Solve the inequality $$(1 - x)(x - 4) < 0$$ [1 mark] Tick \((\checkmark)\) one box. \(\{x : x < 1\} \cup \{x : x > 4\}\) \(\{x : x < 1\} \cap \{x : x > 4\}\) \(\{x : x < 1\} \cup \{x : x \geq 4\}\) \(\{x : x < 1\} \cap \{x : x \geq 4\}\)

Given \((x - 1)(x - 2)(x - a) < 0\) and \(a > 2\) Find the set of possible values of \(x\). Tick \((\checkmark)\) one box. [1 mark] \(\{x : x < 1\} \cup \{x : 2 < x < a\}\) \(\{x : 1 < x < 2\} \cup \{x : x > a\}\) \(\{x : x < -a\} \cup \{x : -2 < x < -1\}\) \(\{x : -a < x < -2\} \cup \{x : x > -1\}\)

Solve the inequality \(x^2 + 3x - 6 > 4x - 4\). [4]

Solve the inequalities

1. \(3 - 8x > 4\), [2]
2. \((2x - 4)(x - 3) < 12\). [5]

In this question you must show detailed reasoning. \includegraphics{figure_5} The diagram shows the cuboid \(ABCDEFGH\) where \(AD = 3\) cm, \(AF = (2x + 1)\) cm and \(DC = (x - 2)\) cm. The volume of the cuboid is at most 9 cm³. Find the range of possible values of \(x\). Give your answer in interval notation. [5]