# Inequality

• May 22nd 2009, 05:28 PM
cam_ddrt
Inequality
I have a couple of problems I cannot figure out. Any help would be greatly appreciated!

1. Solve the inequality |3x-1|> 4. Express your answer in terms of intervals

2. A piece of wire 40 cm. long is cut into 2 pieces. One piece is bent into a square, the other is bent into an equilateral triangle. Express the length, s, of the side of the square in terms of the length, t, of the side of the triangle.
• May 22nd 2009, 06:07 PM
yeongil
Quote:

Originally Posted by cam_ddrt
I have a couple of problems I cannot figure out. Any help would be greatly appreciated!

1. Solve the inequality |3x-1|> 4. Express your answer in terms of intervals

Rewrite the absolute value inequality as a compound inequality:
$\displaystyle 3x - 1 > 4$ OR $\displaystyle 3x - 1 < -4$
Now solve for x:
$\displaystyle 3x > 5$ OR $\displaystyle 3x < -3$
$\displaystyle x > \frac{5}{3}$ OR $\displaystyle x < -1$

In interval notation:
$\displaystyle (-\infty, -1) \cup (5/3, \infty)$

01
• May 22nd 2009, 06:17 PM
yeongil
Quote:

Originally Posted by cam_ddrt
2. A piece of wire 40 cm. long is cut into 2 pieces. One piece is bent into a square, the other is bent into an equilateral triangle. Express the length, s, of the side of the square in terms of the length, t, of the side of the triangle.

Let's say that the length of the piece that was bent into a square is x. Since the perimeter of a square is 4s,
x = 4s or s = x/4.

Since the whole piece of wire is 40cm and the piece bent into a square is x cm, the piece bent into an equilateral triangle would be 40 - x cm. The perimeter of an equilateral triangle is 3t, so 40 - x = 3t. Solve for x:
$\displaystyle 40 - x = 3t$
$\displaystyle 40 = x + 3t$
$\displaystyle 40 - 3t = x$

Plug this into s = x/4:
$\displaystyle s = \frac{40 - 3t}{4}$
$\displaystyle s = 10 - \frac{3}{4}t$

01