Exercise 2 Page 291

We can use an equation mat to solve the inequality $\text{-}4x>\text{-}4.$ However, instead of an equals sign, we must write the inequality symbol $>.$ Let's solve it step by step!

Step $1$

On the left-hand side of the inequality we have $\text{-}4x.$ Therefore, we place $4$ negative $x\text{-}$tiles on one side of the mat. On the right-hand side we have $\text{-}4,$ so we place $4$ negative $1\text{-}$tiles on the other side.

Step $2$

We can eliminate the negative sign by adding $4$ positive $x\text{-}$tiles to each side. Let's do it!

Now, let's remove the zero pairs from the left-hand side.

Step $3$

Next, we can add $4$ positive $1\text{-}$tiles to isolate the $x\text{-}$tiles on the right-hand side.

We formed $4$ zero pairs on the right-hand side.

Step $4$

Finally, we can remove the zero pairs and separate the tiles into $4$ groups. This gives us the following mat.

We can see that each $x\text{-}$tile matches with $1$ positive $1\text{-}$tiles. At last, we can write this inequality algebraically. This is the solution of our inequality.