Pre-U Pre-U 9794/1 2018 June — Question 1 4 marks

Exam BoardPre-U
ModulePre-U 9794/1 (Pre-U Mathematics Paper 1)
Year2018
SessionJune
Marks4
TopicInequalities
TypeSolve absolute value inequality
DifficultyModerate -0.3 This is a straightforward absolute value inequality requiring case analysis (splitting at x = 1/3) and solving two linear inequalities. While it requires systematic method rather than just recall, it's a standard textbook exercise with no conceptual surprises, making it slightly easier than average.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities
1 Solve \(5 x + 3 < | 3 x - 1 |\).
AnswerMarks Guidance
Question 1: Solve \(5x + 3 <3x - 1 \)
\(5x + 3 < -(3x - 1)\) (if \(3x - 1 < 0\)) M1
\(x < -\frac{1}{4}\) A1 (Obtain at least the critical value)
\(5x + 3 < 3x - 1\) (if \(3x - 1 > 0\))
\(\Rightarrow x < -2\) B1
\(x < -\frac{1}{4}\) only A1
*Alternative:* \((5x+3)^2 < \) or \(= (3x-1)^2\) M1
\(x = -2\) or \(x = -\frac{1}{4}\) A1
\(x < -\frac{1}{4}\) only M1A1
Total: 4 marks
**Question 1: Solve $5x + 3 < |3x - 1|$**

$5x + 3 < -(3x - 1)$ (if $3x - 1 < 0$) **M1**

$x < -\frac{1}{4}$ **A1** (Obtain at least the critical value)

$5x + 3 < 3x - 1$ (if $3x - 1 > 0$)
$\Rightarrow x < -2$ **B1**

$x < -\frac{1}{4}$ only **A1**

*Alternative:* $(5x+3)^2 < $ or $= (3x-1)^2$ **M1**
$x = -2$ or $x = -\frac{1}{4}$ **A1**
$x < -\frac{1}{4}$ only **M1A1**

**Total: 4 marks**
1 Solve $5 x + 3 < | 3 x - 1 |$.

\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2018 Q1 [4]}}
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