Question
Asked Nov 26, 2019
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Solve the inequality by using a number line and the behavior of the graph at each zero.
1
c2
Write the solution in interval notation
5
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Solve the inequality by using a number line and the behavior of the graph at each zero. 1 c2 Write the solution in interval notation 5

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Expert Answer

Step 1

Subtract (x-2)/(x-7) then subtract using LCD.

1 х-2
<
x+5
x-7
1
X-2
<O
X-7
х+5
(х-7)-(х-2)(х+5)
<O
(х+5)(х-7)
х-7-(х?+3х-10)
<0
(х+5)(х-7)
х-7-x?-3х+10
<0
(х+5)(х-7)
-x?-2х+3
<0
(х+5)(х-7)
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1 х-2 < x+5 x-7 1 X-2 <O X-7 х+5 (х-7)-(х-2)(х+5) <O (х+5)(х-7) х-7-(х?+3х-10) <0 (х+5)(х-7) х-7-x?-3х+10 <0 (х+5)(х-7) -x?-2х+3 <0 (х+5)(х-7)

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Step 2

Factor the numerator.

 

-x2-2x+3
<0
(x+5)(x-7)
-(x+3)(x-1)
<0
(x+5)(x-7)
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-x2-2x+3 <0 (x+5)(x-7) -(x+3)(x-1) <0 (x+5)(x-7)

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Step 3

We set every factor of the numerator and denominator eq...

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