Answer
$4\leq z$
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 $z+6$.
- 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)
$4\leq z$
