Exercise 4.2 Class 10 Math Solutions – Absolute Value Graphs, Equations & Inequalities, Punjab Board

Solved Exercise 4.2 for Class 10 Mathematics, Punjab Board. Detailed step-by-step notes covering absolute value function graphs, plotting V-shaped curves, solving absolute value linear equations in one variable, and solving absolute value linear inequalities with interval notation.

This page provides complete solved solutions for Exercise 4.2 from Unit 4: Functions and Graphs, Class 10 Mathematics, Punjab Board (PCTB). It covers graphing absolute value functions (f(x) = |ax + b| + c), solving absolute value linear equations (|ax + b| = c ⇒ ax + b = ±c), and solving absolute value linear inequalities (|ax + b| < c ⇒ -c < ax + b < c and |ax + b| > c ⇒ ax + b > c or ax + b < -c). All questions are worked out step by step for Matric Part 2 students.
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Exercise Overview

Exercise 4.2 focuses on absolute value functions, equations, and inequalities in Unit 4: Functions and Graphs for Class 10 Punjab Board Mathematics. Absolute value concepts are fundamental in mathematical analysis, representing geometric distance from zero on the real number line and introducing piecewise-defined functions.

The exercise begins with graphing absolute value functions of the form f(x) = |ax + b| and f(x) = |ax + b| + c. Students learn to locate the vertex, create symmetrical input-output value tables, and sketch the distinct V-shaped piecewise graph. The exercise then covers algebraic solutions: solving absolute value linear equations (|ax + b| = c) by branching into positive and negative cases while testing against extraneous roots, and solving absolute value linear inequalities. Students master both the "less than" conjunction (-c < ax + b < c) and the "greater than" disjunction (ax + b > c or ax + b < -c), expressing solution sets accurately in set-builder and interval notation.

In Punjab Board examinations (such as Lahore, Faisalabad, Rawalpindi, Gujranwala, Multan, and other BISE boards), Exercise 4.2 questions frequently appear in Section B (Short Questions on equations and inequalities) and Section C (Graph plotting and multi-step inequality solutions). Practicing these step-by-step solutions guarantees clarity and precision for high scores in matric board examinations.

FAQs

Are these Exercise 4.2 solutions according to the Punjab Board syllabus?
Yes. These solutions follow the Punjab Curriculum and Textbook Board (PCTB) syllabus for Class 10 Mathematics, covering all Unit 4 Exercise 4.2 absolute value topics for the 2026-2027 session.
What is an absolute value function and what does its graph look like?
An absolute value function is defined by f(x) = |x| = x for x ≥ 0 and -x for x < 0. Its graph forms a characteristic symmetric V-shape with its vertex at the turning point.
How do you solve an absolute value linear equation |ax + b| = c?
If c ≥ 0, set up two linear equations: ax + b = c and ax + b = -c, solve each for x, and check for extraneous solutions. If c < 0, there is no real solution.
How do you solve an inequality of the form |ax + b| < c?
For c > 0, the inequality |ax + b| < c is equivalent to the double inequality -c < ax + b < c, which is solved by isolating x in the middle.
How do you solve an inequality of the form |ax + b| > c?
For c > 0, the inequality |ax + b| > c splits into two separate disjoint inequalities: ax + b > c or ax + b < -c, and the solution set is the union of their intervals.
Why is it important to check for extraneous solutions in absolute value equations?
Because absolute values are non-negative by definition (|u| ≥ 0), substituting potential solutions back into the original equation ensures that negative equal terms do not produce false solutions.
How do you find the vertex of an absolute value graph f(x) = a|x - h| + k?
The vertex of the absolute value function f(x) = a|x - h| + k is the point (h, k), where the graph turns.
Can students read these Exercise 4.2 solutions online?
Yes, the complete solved PDF notes for Exercise 4.2 are embedded to read online directly on MaryamNotes.pk with no compulsory download.
Are these Exercise 4.2 solutions free for students?
Yes, all Exercise 4.2 solutions on MaryamNotes.pk are 100% free to read online for all Class 10 students across all Punjab boards.