SOLUTION: Solve and write using interval notation: -3 < -5x + 7 <= 8

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Question 302032: Solve and write using interval notation: -3 < -5x + 7 <= 8

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
-3+%3C+-5x+%2B+7+%3C=+8
This says 2 things:
(1) -3+%3C+-5x+%2B+7
and
(2) -5x+%2B+7+%3C=+8
Subtract 7 from both sides of (1)
(1) -3+-7+%3C+-5x
(1) -10+%3C+-5x
Divide both sides by -5 and reverse < sign
(1) 2+%3E+x
or,
(1) x+%3C+2
Now subtract 7 from both sides of (2)
-5x+%3C=+1
Divide both sides by -5 and reverse sign
x+%3E=+-1%2F5
Or, what is the same thing:
-1%2F5+%3C=+x
Putting (1) and (2) together:
-1%2F5+%3C=+x+%3C+2 answer