Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 2 - Section 2.5 - Compound Inequalities - Exercise Set - Page 95: 86

Answer

$ (2, \infty ) $

Work Step by Step

We break this into two different inequalities. $$x+3 \lt 2x+1$$ $$and $$ $$ 2x+1 \lt 4x + 6 $$ Then, follow PEMDAS. In other words, first address parentheses, and then resolve exponents. Next, simplify division and multiplication, and lastly address subtraction and addition. This gives: $$x \gt 2$$ $$and $$ $$ x \gt -5/2 $$ We are only considering the intersection of these two sets, so we know that $ (2, \infty ) $ is the correct answer.
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