Wow, can someone help me please? Thanks!

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Answer 1 · 2017-09-09T00:50:59

The solution is A.

$2| x + 1/3 | < 9$

We must solve this for both a positive and negative value in the absolute bars.

For positive value in bars, just remove them.

$2(x + 1/3 ) < 9$

Multiply by 2:

$2x + 2/3 < 9$

Multiply by $3$

$6x + 2 < 27$

Subtract $2$ and divide by $6$

$x <$ 4 $1/6$

For negative value in bars:

$2(-(x + 1/3 )) < 9$

$2(-x - 1/3) <9$

$-2x - 2/3 < 9$

Multiply by 3

$-6x -2 < 27$

Add 2 and divide by $-6$ (reverse inequality sign because of division by negative value)

$x > -$ 4 $5/6$

$-$ 4 $5/6< x <$ 4 $1/6$

Dark blue represents included values.

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