## Algebra 1

$b\gt-4$ 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) $b\gt-4$