## Algebra 1

Published by Prentice Hall

# Chapter 3 - Solving Inequalities - Concept Byte - Modeling Multi-Step Inequalities - Page 185: 8

#### Answer

$b\gt-4$ #### 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 $5b+6$. - A green tile represents a variable such as b. The left side of the diagram will include 5 green tiles since the coefficient of b is 5. - The left side will also include 6 yellow tiles. Each yellow tile represents +1, so adding 6 is represented by 6 yellow tiles. The right side of the equation is $3b-2$. - A green tile represents a variable such as b. The right side of the diagram will include 3 green tiles since the coefficient of b is 3. - The left side will also include 2 red tiles. Each red tile represents -1, so subtracting 2 is represented by 2 red tiles. The steps to solve the inequality algebraically mirror the steps of solving using the tiles. $5b+6\gt3b-2\longrightarrow$ subtract 3b from each side $5b+6-3b\gt3b-2-3b\longrightarrow$ subtract (remove 3 green tiles from each side) $2b+6\gt-2\longrightarrow$ subtract 6 from both sides (6 red tiles) $2b+6-6\gt-2-6\longrightarrow$ subtract (remove zero pairs) $2b\gt-8\longrightarrow$ divide both sides by 2 (identify identical groups) $2b\div2\gt-8\div2\longrightarrow$ divide (remove duplicate groups) $b\gt-4$

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