## Algebra 1

$4\leq z$ 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 $z+6$. - A green tile represents a variable such as z. The left side of the diagram will include 1 green tile since the implied coefficient of z is 1. - 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 $2z+2$. - A green tile represents a variable such as z. The right side of the diagram will include 2 green tiles since the coefficient of z is 2. - The left side will also include 2 yellow tiles. Each yellow tile represents +1, so adding 2 is represented by 2 yellow tiles. The steps to solve the inequality algebraically mirror the steps of solving using the tiles. $z+6\leq2z+2\longrightarrow$ subtract z from each side $z+6-z\leq2z+2-z\longrightarrow$ subtract (remove one green tile from each side) $6\leq z+2\longrightarrow$ subtract 2 from both sides (2 red tiles) $6-2\leq z+2-2\longrightarrow$ subtract (remove zero pairs) $4\leq z$