Question 430062
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))