Exercise 2 Page 291

We can use an equation mat to solve the inequality -4x>-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 -4x. Therefore, we place 4 negative x-tiles on one side of the mat. On the right-hand side we have -4, so we place 4 negative 1-tiles on the other side.

Step 2

We can eliminate the negative sign by adding 4 positive x-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-tiles to isolate the x-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-tile matches with 1 positive 1-tiles. At last, we can write this inequality algebraically. 1 >x ⇔ x < 1 This is the solution of our inequality.