Solve |linear| = constant

1 Solve the equation \(| 0.4 x - 0.8 | = 2\).

1 Candidates answer on the Question Paper.
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The total number of marks for this paper is 50. 1

1. Solve the inequality \(| 2 x - 7 | < | 2 x - 9 |\).
2. Hence find the largest integer \(n\) satisfying the inequality \(| 2 \ln n - 7 | < | 2 \ln n - 9 |\).

1. The function f is defined by

$$\mathrm { f } : x \mapsto | x - 2 | - 3 , x \in \mathbb { R }$$

1. Solve the equation \(\mathrm { f } ( x ) = 1\). The function g is defined by $$\mathrm { g } : x \mapsto x ^ { 2 } - 4 x + 11 , x \geq 0$$
2. Find the range of g .
3. Find \(g f ( - 1 )\).

1 Solve the equation \(| 3 x + 2 | = 1\).

12 Solve the equation \(| 3 x + 2 | = 1\).

7 The functions \(\mathrm { f } , \mathrm { g }\) and h are defined for all real values of \(x\) by $$\mathrm { f } ( x ) = | x | , \quad \mathrm { g } ( x ) = 3 x + 5 \quad \text { and } \quad \mathrm { h } ( x ) = \mathrm { gg } ( x ) .$$

1. Solve the equation \(\mathrm { g } ( x + 2 ) = \mathrm { f } ( - 12 )\).
2. Find \(\mathrm { h } ^ { - 1 } ( x )\).
3. Determine the values of \(x\) for which $$x + \mathrm { f } ( x ) = 0 .$$

2 Solve the equation \(| x + 3 | = 5\).

Solve the equation \(|3x + 2| = 1\).

Solve the equation \(|2x - 3| = 9\). [3]