Unit Name: Polynomial and Rational Functions Solve the following inequality algebraically.

Juan Hewlett 2021-12-11 Answered
Unit Name: Polynomial and Rational Functions
Solve the following inequality algebraically. Explain your process.
8x32x+117x8
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Expert Answer

Karen Robbins
Answered 2021-12-12 Author has 49 answers
Split the inequality into two:
8x32x+1 and 2x+117x8
Isolate x from each inequality using inverse operations.
8x32x+1
8x2x3+1
6x4
x23
AND
2x+117x8
2x17x81
15x+15x9+15x
09+15x
35x
Therefore, the solution is: 35x23
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Shannon Hodgkinson
Answered 2021-12-13 Author has 34 answers
Solve the following inequality algebraically.
Explain your process.
8x32x+117x8
We've 8x32x+117x8. (1)
8x312x+1117x81
8x42x17x9
Now dividing above equation by 2 we get
8x422x2172x92
4x2x172x92 (2)
Now from equation (2) we've two cases.
(1) x4x2
adding 2 to both sides we get
x+24x2+2
x+24x
Subtracting x from both sides
x+2x4xx
23x
x23
x172x92
adding 92 to both sides we get
x+92172x92+92
x+92172x
Subtracting x from both sides
x+92x172xx
q217x2x2
9215x2
Multiplying 2 to both sides we get
Undefined control sequence \cancel
915x
x35 (4)
From equation (3) and equation (4) we get
35x23
0.6x0.6666
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