Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 2 - Solving Linear Inequalities - 2.2 - Solving Inequalities Using Addition or Subtraction - Monitoring Progress - Page 62: 3

Answer

$y<\frac{1}{2}$ Refer to the graph below.

Work Step by Step

Add $\frac{1}{4}$ to each side: $\begin{align*} \frac{1}{4}+\frac{1}{4}&>y-\frac{1}{4}+\frac{1}{4}\\ \frac{2}{4}&>y\\ \frac{1}{2}&>y \end{align*}$ Note that the inequality above is equivalent to $y<\frac{1}{2}$. Use $0$ as a test number: $\begin{align*} y&<\frac{1}{2}\\ 0&<\frac{1}{2} \end{align*}$ The statement above is true so shade the region where $0$ is located. Use an open circle to obtain the graph below.
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