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Question 430062: solve -1 < 4-5x/2 is less than or equal to 7
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! PLEASE PUT PARENTHASES AROUND THE EQUATION, WITHIN THE EQUATION. WITHOUT THEM, WE CANNOT DETERMINE HOW TO PROPERLY SET UP THE ORIGIONAL.
-1<(4-5x)/(2)<=7
Reorder the polynomial 4-5x alphabetically from left to right, starting with the highest order term.
-1<(-5x+4)/(2)<=7
Multiply each term in the inequality by 2.
-1*2<(-5x+4)/(2)*2<=7*2
Multiply -1 by 2 to get -2.
-2<(-5x+4)/(2)*2<=7*2
Cancel the common factor of 2 from the denominator of the first expression and the numerator of the second expression.
-2<(-5x+4)<=7*2
Remove the parentheses around the expression -5x+4.
-2<-5x+4<=7*2
Multiply 7 by 2 to get 14.
-2<-5x+4<=14
Move all terms not containing x from the center section of the interval inequality.
-2-4<-5x<=14-4
Subtract 4 from -2 to get -6.
-6<-5x<=14-4
Subtract 4 from 14 to get 10.
-6<-5x<=10
Divide each term in the inequality by -5.
-(6)/(-5)>-(5x)/(-5)>=(10)/(-5)
Move the minus sign from the denominator to the front of the expression.
-(-(6)/(5))>-(5x)/(-5)>=(10)/(-5)
Multiply -1 by each term inside the parentheses.
(6)/(5)>-(5x)/(-5)>=(10)/(-5)
Move the minus sign from the denominator to the front of the expression.
(6)/(5)>-(-(5x)/(5))>=(10)/(-5)
Reduce the expression -(5x)/(5) by removing a factor of 5 from the numerator and denominator.
(6)/(5)>-(-x)>=(10)/(-5)
Multiply -1 by each term inside the parentheses.
(6)/(5)>x>=(10)/(-5)
Move the minus sign from the denominator to the front of the expression.
(6)/(5)>x>=-((10)/(5))
Reduce the expression (10)/(5) by removing a factor of 5 from the numerator and denominator.
(6)/(5)>x>=-(2)
Multiply -1 by the 2 inside the parentheses.
(6)/(5)>x>=-2
Rewrite the interval so that the left-hand value is less than the right-hand value. This is the correct way to write an interval solution.
-2<=x<(6)/(5)
Convert the solution to set notation.
[-2,(6)/(5))
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