# Compound Inequality

• January 22nd 2010, 09:36 AM
baka
Compound Inequality
If 3 < x < 4 then

a. | x - 7 | < 3
b. | x - 5 | < 2
c. | x - 4 | < 3
d. | x - 3 | < 4
e. | x - 2 | < 5

I need help solving this.
• January 22nd 2010, 10:57 AM
Hello baka

Welcome to Math Help Forum!
Quote:

Originally Posted by baka
If 3 < x < 4 then

a. | x - 7 | < 3
b. | x - 5 | < 2
c. | x - 4 | < 3
d. | x - 3 | < 4
e. | x - 2 | < 5

I need help solving this.

Try giving $x$ the values at the ends of the interval and see what happens. So:
If $x = 3$:
a. $x-7 = -4 \Rightarrow |x-7| = 4$

b. $x-5 =-2 \Rightarrow |x-2|= 2$

... and so on.
If $x = 4$:
a. $x-7 = -3\Rightarrow |x-7|=3$

b. $x-5 =-1 \Rightarrow |x-2|= 1$

... and so on.
Can you see which of a to e will be correct? (There's more than one correct answer.)