Inequalities Interval Notation
posted by Sasha .
Solve: (2 + x)(5 + x)(4  x) < 0 (write answer in interval notation)
Which I think is xe (infinity, 5) or (2, 4)
and
Solve: (4x + 1)(3  x) > or equal to 0 (write answer in interval notation)
Which im unsure

Inequalities Interval Notation 
Jai
#1.
(2 + x)(5 + x)(4  x) < 0
Equate each term inside the parenthesis to zero:
2 + x < 0
x < 2
5 + x < 0
x < 5
4  x < 0
4 < x
x > 4
When x > 4, only the term (4  x) is negative while the others are positive, so it satisfies the inequality.
When x < 5, say x = 6,
(2  6)(5  6)(4 + 6) < 0
4 * 1 * 10 < 0
40 < 0
which is false. So x cannot be less than or equal to 5.
When x < 2 but greater than 5, say x = 3
(2  3)(5  3)(4 + 3) < 0
1 * 2 * 7 < 0
14 < 0
which is true. So 5 < x < 2. Combine it with x > 4, we'll have
(5, 2) U (4, +infinity)
#2.
(4x + 1)(3  x) ≥ 0
Same procedure we'll do. Equate each term to zero:
4x + 1 ≥ 0
4x ≥ 1
x ≥ 1/4
3  x ≥ 0
3 ≥ x
We get the intersection. So x must be greater than or equal to 1/4 but less than or equal to 3:
[1/4 , 3]
hope this helps~ `u` 
Inequalities Interval Notation 
Steve
After you get a bit of practice with this kind of stuff, you can feel confident using what you know about the graphs of polynomials.
(2 + x)(5 + x)(4  x) < 0
You know this is a cubic, with three roots. The graph crosses the xaxis at each root. So, pick a very large negative value for x.
The product ()()(+) is positive
So, you know that the graph crosses below the xaxis at 5 back up at 2 and back down at 4. So, f(x) < 0 on
(5,2)U(4,∞)
Respond to this Question
Similar Questions

calculus
We were asked to solve the problem 1/x < 4. I solved it like so: 1<4x 1/4<x and wrote my answer in interval notation as (1/4, infinity). However, the answer in the back of my book said the answer was the union between (negative … 
Algebra
Solve 9 – 4x > 7 and write interval notation for the solution set. A.(1/2, 4) B. (4,1/2) C. (1/2, infinity) D. (infinity U (4, infinity) I say the answer is D..Am i correct? 
Algebra
Solve x(x7)(x9)<0 and express the solution set in interval notation. A. (–infinity, 0) B. (–infinity, 0) U (7, 9) C. (–infinity, 0) U (9, infinity) D. (–infinity, 9) 
Algebra
Solve and express in interval notation Solve: 5 – 8x > 11 and write interval notation for the solution set. This is what I get but I need it in interval notation. x<3/4 or x >2 Solve: (x3)/(x^225)<0 and write interval … 
Math Help Please
Please show me how to put this in interval notation. Thanks! I know I solved this right, I think, but need to put it in interval notatioin. Please tell me if i am correct. Thanks! PleaseSolve: (x3)/(x^225)<0 and write solution … 
mathinequalities
Hi, I am having some problems with inequalities. It is asking us to solve and graph on a number line and then write it in interval notation and set notation. X>2 and X>4 I graphed them in a number line already and i have the … 
math
Please help. Hi, I am having some problems with inequalities. It is asking us to solve and graph on a number line and then write it in interval notation and set notation. X>2 and X>4 I graphed them in a number line already and … 
Solve Inequality
Solve the inequality. Express your solution using interval notation and please show all of your work. x(x + 6)(8 – x) >= 0 I need help, I guess I'm not understanding the interval notation portion. I know, that when 0 <= x <= … 
Math
Solve the compound inequalities. Write the solutions in interval notation. Graph your solution on a number line. 1. 2(3x + 1)< 10 or 3(2x  4) ¡Ý 0 The or means union of these inequalities. 2. 5(p + 3) + 4 > p  1 or 4(p  … 
AlgebraInterval Notation
I don't remember how to solve this. The question is: For what values of a is the expression 7(x2)5 negative?