Algebra 1

Published by Prentice Hall
ISBN 10: 0133500403
ISBN 13: 978-0-13350-040-0

Chapter 3 - Solving Inequalities - Concept Byte - Modeling Multi-Step Inequalities: 1

Answer

$3x+5 > -4$ $ x > -3$

Work Step by Step

Each side of the diagram represents one side of the equation. The bar separating the two sides represents the inequality sign. The left side of the equation is 3x+5. - Green tiles represent the variable, such as x. The left side of the diagram includes three green tiles since the coefficient of x is 3. - The left side will also include 5 yellow tiles. Each yellow tile represents 1, so adding 5 is represented by 5 yellow tiles. The right side of the equation is -4. - A red tile represents -1, so 4 is represented by 4 red tiles. The steps to solve the equation algebraically mimic the steps using the tiles. $3x+5\gt-4$ (starting inequality) $3x+5 (-5) \gt -4 (-5)$ (subtract 5 from both sides, 5 red tiles) $3x \gt -9$ (removing zero pairs) $\frac{3x}{3} \gt \frac{-9}{3}$ (dividing both sides by 3, find identical groups and remove identical groups) $x \gt -3$
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