Sunday

April 20, 2014

April 20, 2014

Posted by **peter** on Monday, June 14, 2010 at 2:31pm.

4 < 2x+1/x-3 < 7

- math -
**Reiny**, Monday, June 14, 2010 at 6:10pmmultiply by x-3

4(x-3) < 2x + 1 < 7(x-3) , if x-3 > 0 or x > 3

4x-12 < 2x+1 or 2x+1 < 7x - 21

2x < 13 ----- or -5x < -22

x < 6.5 ------ or x > 22/5

So we have 3 critical values, x = 6.5 , x = 4.4 and x = 3

dividing our number line into 4 segments.

I then take any value in each of the segments and test it in the original

left segment , x < 3, e.g let x = 0

4 < 1/-3 < 7 false

segment between 3 and 4.4, x = 4

4 < 9/1 < 7 false

segment between 4.4 and 6.5, x = 5

4 < 11/2<7

4<5.5<7 true

segment > 6.5, x = 10

4 < 21/8<7

4 < 2.625<7 false

so 4.4 < x < 6.5

btw, if you have a graphing calculator

graph

y = (2x+1)(x-3) , y = 4 and y = 7 and you will see that they intersect at (4.4 , 7) and (6.5 , 4)

so the graph is between 4 and 7 for my values

**Related Questions**

algebra 1 - who is correct and why? chloe jonas 3<2x-5<7 3<2x-5<7 3&...

Algebra/Pre-Calc - Find the values for a and b such that f(x) is continuous on ...

math - < = Angle <R and <S are complementary angles, and <U and <...

math - Ex 3: 4x-7<2x+5 4x-7-2x<2x-2x+5 2x-7<5 2x-7+7<5+7 2x<12 2x...

math - Identify the domain and range of the following: f(x) = 4-x^2, -5<x<...

math 234 calc 4 !!!!!!!!!!! - write this function in terms of heaviside ...

math - i need help with these problems please [6-2x]<4 which is the numeral ...

math b - i need help with these problems please [6-2x]<4 which is the numeral...

advance algebra - 1. 2(6x+13)-7 >= 21 ">=" is greater than or equal <= ...

Math - <L and <M are complementary angles. <N and <P are ...