The solution set for: $(x + 3) + 4 > - 2 x + 5$ .

(- \frac{2}{3}, \infty)

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(\frac{2}{3}, \infty)

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(- \infty, - \frac{2}{3})

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(- \frac{2}{3}, 2)

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Solution

The correct option is A $(- \frac{2}{3}, \infty)$
$(x + 3) + 4 > - 2 x + 5$
$\Rightarrow x + 3 + 4 > - 2 x + 5$
Add $2 x, - 3$ and $- 4$ , we get
$x + 3 + 4 + 2 x - 3 - 4 > - 2 x + 5 + 2 x - 3 - 4$
$\Rightarrow x + 2 x > 5 - 3 - 4$
$\Rightarrow 3 x > - 2$
Dividing by $3,$ we get
$x > - \frac{2}{3}$
Then x is $(- \frac{2}{3}, \infty)$

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