## Question 9:

| $|2x-1| \leq 3$ | | |
|---|---|---|
| $\Rightarrow -3 \leq 2x-1 \leq 3$ | | |
| $\Rightarrow -2 \leq 2x \leq 4$ | | |
| $\Rightarrow -1 \leq x \leq 2$ | | |
| $2x-1 \leq 3$ (or $=$) | M1 | |
| $x \leq 2$ | A1 | |
| $2x-1 \geq -3$ (or $=$) | M1 | |
| $x \geq -1$ | A1 | |
| *or* $(2x-1)^2 \leq 9$ | M1 | squaring and forming quadratic $= 0$ (or $\leq$) |
| $\Rightarrow 4x^2 - 4x - 8 \leq 0$ | | |
| $\Rightarrow (4)(x+1)(x-2) \leq 0$ | A1 | factorising or solving to get $x = -1, 2$ |
| $\Rightarrow -1 \leq x \leq 2$ | A1 | $x \geq -1$ |
| | A1 | $x \leq 2$ (www) |
| **[4]** | | |

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