SOLUTION: If (x+1)(x-2) is positive, which statement must be true? A. x<-1 or x>2 B. x>-1 or x<2 C. -1<x<2 D. -2<x<1

Algebra.Com
Question 1151023: If (x+1)(x-2) is positive, which statement must be true?
A. x<-1 or x>2
B. x>-1 or x<2
C. -1 D. -2
Found 3 solutions by MathLover1, jim_thompson5910, greenestamps:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

If is positive, means
if =>
if =>


interval:
(, ) U (, )
Identify the intervals that satisfy the required condition: >:
or

answer:
A. or

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

A shorthand way of saying "(x+1)(x-2) is positive" is to write (x+1)(x-2) > 0

Change the inequality sign to an equal sign. Then solve for x using the zero product property.

(x+1)(x-2) = 0
x+1 = 0 or x-2 = 0
x = -1 or x = 2

If x = -1 or x = 2, then (x+1)(x-2) is equal to zero.

Draw a number line. Plot -1 and 2 on the number line. This drawing is optional, but it might help you see the three distinct regions.

Region A in red represents everything to the left of -1.
Let's pick one value from this region, say x = -2
(x+1)(x-2) > 0
(-2+1)(-2-2) > 0 ... plug in x = -2
(-1)(-4) > 0
4 > 0
The last inequality is true, so any value less than -1 will make (x+1)(x-2) > 0 true.

Move onto region B in blue. This is the set of numbers between -1 and 2. Pick something from this region, say x = 0, and plug it in to get
(x+1)(x-2) > 0
(0+1)(0-2) > 0
(1)(-2) > 0
-2 > 0
The last inequality is false, so any value between -1 and 2 will make (x+1)(x-2) > 0 false.

Finally let's check region C in green. Pick a value to the right of 2. I'll pick x = 3.
(x+1)(x-2) > 0
(3+1)(3-2) > 0
(4)(1) > 0
4 > 0
The last inequality is true, so any value larger than 2 will make (x+1)(x-2) > 0 true.

---------------------------------------------

So,


This is why the final answer is A. x < -1 or x > 2
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


(x+1)(x-2) is positive if (a) both factors are positive, or (b) both factors are negative.

The product is zero only at x = -1 and x = 2.
Both factors are positive only when x > 2.
Both factors are negative only when x < -1.

ANSWER: x < -1 OR x > 2. Answer choice A.
RELATED QUESTIONS

If (x + 1)(x ­- 2) is positive, which statement is true? x < -­ 1 or x > 2 x > - ­1... (answered by fractalier)
0 < x < 10, and x ≠ 1.Which of the following must be true? A) x^2 > x B) x^2 >... (answered by susanaramya)
If x is a positive integer, which of the following CANNOT be an integer? (A) {{{... (answered by JimboP1977,comfuse,ikleyn,greenestamps)
The expression ( x + 1)(x + 2) > 0 is equivalent to which of the following? (a) All of (answered by Edwin McCravy)
Fill in the blanks: a) For the expression 1 over the square root of x-2 to have real... (answered by rapaljer)
25 if x squared-x-6=0 then x is: A) -2 or 3 B) -1 or 6 C) 1 or -6 D) 2 or... (answered by ptaylor)
find all the real number that satisfy the inequality 1 (answered by Timnewman,Fombitz)
If 2xy=0 and x/2 = 3/4, which of the following must be true? 1. 2y=-3 2. x=-12y 3.... (answered by stanbon)
The interval where fx) = -2(x+2)(x-3)(x-1) is positive will be A) x > 0 B) -2 < x < 1, (answered by MathLover1,solver91311,ikleyn)