Solve equations and inequalities 1 ) 5 x 2 </msup>

motorinum6fh9v

motorinum6fh9v

Answered question

2022-05-14

Solve equations and inequalities
1 ) 5 x 2 + 2 x + 5 x + 2 = 5 x + 1
2 ) 2 x + 10 x + 8 > 4 x + 8 2

Answer & Explanation

hodowlanyb1rq2

hodowlanyb1rq2

Beginner2022-05-15Added 12 answers

1 ) 5 x 2 + 2 x + 5 x + 2 = 5 x + 1
then, 5 x 2 + 2 x + 5 = ( 5 x + 1 ) ( x + 2 )
5 x 2 + 2 x + 5 = 5 x 2 + 10 x + x + 2
5 x 2 + 2 x + 5 = 5 x 2 + 11 x + 2
5 x 2 + 2 x + 5 5 x 2 11 x 2 = 0
9 x + 3 = 0
9 x = 3
x = 3 9
x = 1 3
Consider 2 ) 2 x + 10 x + 8 > 4 x + 8 2
2 x + 10 x + 8 > 4 2 ( x + 8 ) x + 8
2 x + 10 x + 8 > 4 2 x + 16 ) x + 8
2 x + 10 x + 8 > 2 x + 12 x + 8
2 x + 10 x + 8 + 2 x + 12 x + 8 > 0
2 x + 10 + 2 x + 12 x + 8 > 0
4 x + 22 x + 8 > 0
2 x ( x + 11 ) x + 8 > 0
x + 11 x + 8 > 0
When x + 11 > 0 and x + 8 > 0,
So, x 11 > 0 and x 8 > 0,
Therefore, x > 8
Now, when x + 11 < 0 and x + 8 < 0
So, x 11 < 0 and x 8 < 0
Therfore, x < 11
Thus, the answer is ( , 11 ) ( 8 , )

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