Question

Question #3b0b6

Answer 1

Of the four possible answers given, NONE are similar.

Explanation:

We are given the expression: `x < y < z`

We are asked which of the following expressions are `similar`.
That means which one will give us a result that matches the original `given` expression:

1) `(z – y) > x`
2) `(x + z) < y`
3) `(x + y) > z`
4) `(y – x) > z`

To understand this concept we will substitute some numbers as an example of evaluating this expression:

We can say that: `x < y < z color(red)(= 1 < 2 < 3)`

where we have made: `x = 1; y = 2; z =3`

Looking at the numbers we have substituted in, we can see that this expression can also be written as:

`z > y> x color(red)(= 3 > 2 > 1)`

Before panic sets in, we are only re-arranging the `given` expression to easily compare it to the other four.

As you can see by the numbers, all we have done is reverse their order, but in doing so we had to reverse the signs of the inequality to keep everything correct.

Now we can evaluate the four expressions by substituting the same number values as above into 1), 2), 3), 4):

1) `(z – y) > x color(red)(= (3 - 2) > 1 = 1 > 1)` so this expression is not valid

2) `(x + z) < y color(red)(= (1 + 3) < 2 = 4 < 2)` so this expression is not valid

3) `(x + y) > z color(red)(= (1 + 2) > 3 = 3 > 3)` so this expression is not valid

4) `(y - x) > z color(red)(= (2-1) > 3 = 1 > 3)` so this expression is not valid

So none of the triangles in the four expressions will match the original, so there is no similarity.