Question 345348: Solve Inequality
Express the answer in terms of intervals, if possible.
(5x + 1)(8 - 16x) > 0 Found 2 solutions by haileytucki, MathTherapy:Answer by haileytucki(390) (Show Source):
You can put this solution on YOUR website! (5x+1)(8-16x)>0
If any individual factor on the left-hand side of the equation is equal to 0, the entire expression will be equal to 0.
(5x+1)=0_(8-16x)=0
Set the first factor equal to 0 and solve.
(5x+1)=0
Remove the parentheses around the expression 5x+1.
5x+1=0
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
5x=-1
Divide each term in the equation by 5.
(5x)/(5)=-(1)/(5)
Simplify the left-hand side of the equation by canceling the common factors.
x=-(1)/(5)
Set the next factor equal to 0 and solve.
(8-16x)=0
Factor out the GCF of 8 from each term in the polynomial.
(8(1)+8(-2x))=0
Factor out the GCF of 8 from 8-16x.
(8(1-2x))=0
Divide both sides of the equation by 8. Dividing 0 by any non-zero number is 0.
(1-2x)=0
Set each of the factors of the left-hand side of the equation equal to 0.
1-2x=0
Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 1 from both sides.
-2x=-1
Divide each term in the equation by -2.
-(2x)/(-2)=-(1)/(-2)
Simplify the left-hand side of the equation by canceling the common factors.
x=-(1)/(-2)
Simplify the right-hand side of the equation by simplifying each term.
x=(1)/(2)
To find the solution set that makes the expression greater than 0, break the set into real number intervals based on the values found earlier.
x<-(1)/(5)_-(1)/(5)
Determine if the given interval makes each factor positive or negative. If the number of negative factors is odd, then the entire expression over this interval is negative. If the number of negative factors is even, then the entire expression over this interval is positive.
x<-(1)/(5) makes the expression positive_-(1)/(5)
Since this is a 'greater than 0' inequality, all intervals that make the expression positive are part of the solution.
x<-(1)/(5) or x>(1)/(2)
