OCR C3 — Question 2 5 marks

Exam BoardOCR
ModuleC3 (Core Mathematics 3)
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicInequalities
TypeSolve absolute value inequality
DifficultyStandard +0.8 This modulus inequality requires systematic case analysis by considering critical points x = -1/3 and x = 2, then solving and checking validity in each region. While the technique is standard C3 content, the need to square both sides or carefully handle four cases, then combine solution sets correctly, makes this moderately harder than average—requiring careful algebraic manipulation and logical reasoning beyond routine exercises.
Spec1.02g Inequalities: linear and quadratic in single variable1.02l Modulus function: notation, relations, equations and inequalities

Find the set of values of \(x\) such that $$|3x + 1| \leq |x - 2|.$$ [5]

Find the set of values of $x$ such that
$$|3x + 1| \leq |x - 2|.$$ [5]

\hfill \mbox{\textit{OCR C3  Q2 [5]}}