Exercise 2 Page 90

We can use an equation model to solve $2x+5=9.$ Let's do it step by step!

Step $1$

We can begin with modeling the equation. On the left-hand side we have $2x+5,$ so we place $2$ $x\text{-}$tiles and $5$ positive $1\text{-}$tiles on one side of the mat. On the other side, we place $9$ positive $1\text{-}$tiles.

Step $2$

Now, we want to isolate the $x\text{-}$term. Since there are $5$ positive $1$-tiles with the $x\text{-}$tiles, we can add $5$ negative $1$-tiles to each side to form the zero pairs.

Step $3$

Next, we can group the tiles to show the zero pairs. There are $5$ of them on each side.

Let's remove the zero pairs!

Step $4$

Finally, we can group the remaining tiles into $2$ equal groups to match the $x\text{-}$tiles.

We can tell that each $x\text{-}$tile is paired with $2$ positive $1$-tiles. Therefore, the resulting equation is $x=2.$