I used to teach a rather simple way to solve inequalities if they are factored.
in your case (x+20)(x-12)(x+4)>0
so we have 3 "critical" values
x = -20
x = -4
x = 12
marks these values on a number line, giving you 4 regions of numbers
1. for x<-20, pick any number in that region, work out the multiplication only considering the sign, not the actual answer
e.g. x = -30
(-)(-)(-) < 0 , no good
2. let x = -5 , between -20 and -4
(+)(-)(-) > 0 , good one
3. let x = 0 , between -4 and 12
(+)(-)(+) < 0 , no good
4. let x= 20 , greater than 12
(+)(+)(+) > 0 , good
so the result is positive between -20 and 4 as well as greater than 12
-20 < x < -4 OR x > 12
this method also works if you have division mixed in as well.
Of course if you know what the graph looks like, in this case a typical cubic with a + x^3 term, and you know the x-intercepts, you can just state the answer.
The problem to solve is:
(x+20)(x-12)(x+4)>0 but I can't figure out how to do this right so I left off the >0 and tried to solve the equation.
x+20 evaluates to x+20
x-12 evaluates to x-12
Multiplying x+20 by x-12 is a classic Algebra problem. Here, you are trying
to multiply two binomials together (two expressions that each contain two terms).
Your book might call this finding the "Product of Two Binomials".
To work this problem, we'll use the "F.O.I.L." method. F.O.I.L. stands
for First, Outer, Inner, Last.
First, we'll multiply the two First terms, the x and x together.
Multiply x and x
Multiply the x and x
Multiply x and x
Combine the x and x by adding the exponents, and keeping the x, to get
The answer is
x × x =
Second, we'll multiply the two Outer terms, the x and -12 together.
Multiply x and -12
Multiply x and 1
The x just gets copied along.
The answer is x
x
x × -12 = -12x
Third, we'll multiply the two Inner terms, the 20 and x together.
Multiply 20 and x
Multiply 1 and x
The x just gets copied along.
x
20 × x = 20x
-12x combines with 20x to give 8x
Lastly, we'll multiply the two Last terms, the 20 and -12 together.
Multiply 20 and -12
1
20 × -12 = -240
(x+20)*(x-12) evaluates to
x+4 evaluates to x+4
Multiply by x+4
we multiply by each term in x+4 term by term.
This is the distributive property of multiplication.
Multiply and x
Multiply the and x
Multiply and x
Combine the and x by adding the exponents, and keeping the x, to get
The answer is
× x =
Multiply and 4
Multiply and 1
The just gets copied along.
The answer is
× 4 =
Multiply 8x and x
Multiply the x and x
Multiply x and x
Combine the x and x by adding the exponents, and keeping the x, to get
The answer is
8x × x =
combines with to give
Multiply 8x and 4
Multiply x and 1
The x just gets copied along.
The answer is x
x
8x × 4 = 32x
Multiply -240 and x
Multiply 1 and x
The x just gets copied along.
x
-240 × x = -240x
32x combines with -240x to give -208x
Multiply -240 and 4
1
-240 × 4 = -960
(x+20)*(x-12)*(x+4) evaluates to
x^3+12x^2-208x-960?
2 answers
Thank you Reiny
1 answer