You can put this solution on YOUR website! 7 > 5-x > 6
this is really 2 inequalities.
first inequality is 7 > 5-x
second inequality is 5-x > 6
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i believe you need to solve them separately first and then combine them later.
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solve for 7 > 5-x first.
subtract 5 from both sides to get
2 > -x
multiply both sides by -1 to get
-2 < x
notice that the inequality sign is reversed when you multiply by -1.
that takes care of the first inequality.
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solve for 5-x > 6 next.
subtract 5 from both sides to get
-x > 1
multiply both sides by -1 to get
x < -1
notice again that the inequality sign is reversed when you multiply by -1.
that takes care of the second inequality.
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you now have two separate inequalities that both refer to value of x.
-2 < x
x < 1
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since the x on the right of the first equation equals the x on the left of the second equation, you can combine them to get
-2 < x < -1
this means x has to be greater than -2 and less then -1.
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to prove this is true.
take x=-2 and substitute in original equation.
7 > 5-x > 6 becomes 7 > 5-(-2) > 6 becomes 7 > 5+2 > 6 becomes 7 > 7 > 6 equals contradiction therefore x = -2 is no good.
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next take x=-1 and substitute in original equation.
7 > 5-x > 6 becomes 7 > 5-(-1) > 6 becomes 7 > 5+1 > 6 becomes 7 > 6 > 6 equals contradiction therefore x = -1 is no good.
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next take x = any number between -2 and -1 but not including -2 or -1.
take x=-1.9
7 > 5-x > 6 becomes 7 > 5-(-1.9) > 6 becomes 7 > 5+1.9 > 6 becomes 7 > 6.9 > 6 which is not contradictory therefore x = -1.9 is good.
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solution is
-2 < x < -1
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note:
you could also look at values of x < -2 and values of x > -1 to test to see if those are true.
i'll just take one.
let x = -10
7 > 5-x > 6 becomes 7 > 5-(-10) > 6 becomes 7 > 15 > 6 equals a contradiction therefore x = -10 is no good.
you should get the same result if you take any x > -1.
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