Question

What is the sum of the solutions of 2|x-1|-4=-2

The sides of a triangle are in the ratio 3 : 4 : 5. What is the length of each side if the perimeter of the triangle is 90 cm?
a. 19.3 cm, 25.7 cm, and 32.1 cm
b. 7.5 cm, 11.5 cm, and 32.1 cm
c. 10.5 cm, 11.5 cm, and 12.5 cm
d. 22.5 cm, 30 cm, and 37.5 cm

Answer 1

2 |x-1| - 4 = -2

Add 4 to each side: 2 |x-1| = 2

Divide each side by 2 : |x-1| = 1

Possibility #1: x - 1 = 1
Add 1 to each side: x = 2

Possibility #2: x - 1 = -1
Add 1 to each side: x = 0

The sum of the solutions is (2 + 0) = 2 .

=============================================

The lengths of the sides of the triangle are made of
3 shares, 4 shares, and 5 shares.
All together, there are (3+4+5) = 12 shares.
Those 12 shares add up to 90 cm, so each share is (90/12) = 7.5 cm.

3 shares = (3 x 7.5cm) = 22.5 cm
4 shares = (4 x 7.5cm) = 30 cm
5 shares = (5 x 7.5cm) = 37.5cm

Check: Sum = 90 cm yay!