## Algebra 1

$m\geq-6$ 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 $3m+7$. - A green tile represents a variable such as m. The left side of the diagram will include 3 green tiles since the coefficient of m is 3. - The left side will also include 7 yellow tiles. Each yellow tile represents +1, so adding 7 is represented by 7 yellow tiles. The right side of the equation is $m-5$. - A green tile represents a variable such as m. The right side of the diagram will include 1 green tile since the implied coefficient of m is 1. - The left side will also include 5 red tiles. Each red tile represents -1, so subtracting 5 is represented by 1 red tile. The steps to solve the inequality algebraically mirror the steps of solving using the tiles. $3m+7\geq m-5\longrightarrow$ subtract m from each side $3m+7-m\geq m-5-m\longrightarrow$ subtract (remove one green tile from each side) $2m+7\geq-5\longrightarrow$ subtract 7 from both sides (7 red tiles) $2m+7-7\geq-5-7\longrightarrow$ subtract (remove zero pairs) $2m\geq-12\longrightarrow$ divide both sides by 2 (identify identical groups) $2m\div2\geq-12\div2\longrightarrow$ divide (remove duplicate groups) $m\geq-6$