# Solving Inequalities and Representation in Interval Notation## Problem 3### InstructionsSolve the following inequalities and represent the solution in interval notation. Show your work!### Given Inequalities**(a)** $ 6x^2 - 4 \geq 5x + 2 $**(b)** $ x|x - 4| < 3 $### Solution#### Part (a): Quadratic InequalityTo solve the inequality $ 6x^2 - 4 \geq 5x + 2 $:1. Rewrite the inequality in standard form. \[ 6x^2 - 4 \geq 5x + 2 \implies 6x^2 - 5x - 6 \geq 0 \]2. Factor the quadratic expression on the left-hand side (if possible) or use the quadratic formula to find the critical points.3. Determine the intervals to test for the inequality.4. Represent the solution in interval notation.#### Part (b): Absolute Value InequalityTo solve the inequality $ x|x - 4| < 3 $:1. Consider the definition of absolute value and break the problem into cases: - Case 1: $ x \geq 4 $ (where $ |x - 4| = x - 4 $) - Case 2: $ x < 4 $ (where $ |x - 4| = 4 - x $)2. Solve each case separately for $ x \cdot (x - 4) < 3 $ and $ x \cdot (4 - x) < 3 $.3. Combine the results from both cases and represent the solution in interval notation.### Graphical RepresentationsThe graphical representation of the solutions (if applicable) provides a visual aid to understanding the intervals where these inequalities hold true.For further details, including step-by-step solutions, refer to the respective sections on solving quadratic and absolute value inequalities.

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Answered: 3. Solve the following inequalities and…

3. Solve the following inequalities and represent the solution in interval notation. Show your work! (a) 6x? – 4 > 5x + 2

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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