Write an expression in terms of x that represents the positive difference of the lengths of these two sides of the triangle.

Question

The Triangle Inequality has two forms.

1. The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
2. The length of any side of a triangle must lie between the sum and difference of the lengths of the other two sides.

Suppose the lengths of two sides of a triangle are represented by 2x + 7

 and 3x + 9  (assume x is positive).

Write an expression in terms of x that represents the positive difference of the lengths of these two sides of the triangle.

Answer 1

"Difference" indicates subtraction. Since x is positive and since 9 is greater than 7, you will get a positive difference (rather than a negative one) if you subtract (2x + 7) from (3x + 9).

Alyssa, I'll set up the problem and allow you to do the rest. Just remember to distribute the subtraction over each term inside the parentheses that follows the sign.

(3x + 9) — (2x + 7)