Question #38483

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Answer 1 · 2016-09-07T17:05:41

$x > \frac{39}{11}$ $x > (39) / (11)$

We have: $\frac{2}{3} (6 - x) < \frac{1}{4} (x + 3)$ $(2) / (3) (6 - x) < (1) / (4) (x + 3)$

First, let's cross-multiply:

$\Rightarrow 8 (6 - x) < 3 (x + 3)$ $=> 8 (6 - x) < 3 (x + 3)$

Then, let's expand the parentheses:

$\Rightarrow 48 - 8 x < 3 x + 9$ $=> 48 - 8 x < 3 x + 9$

Next, let's subtract $9$ $9$ from both sides:

$\Rightarrow 39 - 8 x < 3 x$ $=> 39 - 8 x < 3 x$

$\Rightarrow 3 x > 39 - 8 x$ $=> 3 x > 39 - 8 x$

Now, let's add $8 x$ $8 x$ to both sides:

$\Rightarrow 11 x > 39$ $=> 11 x > 39$

Finally, let's divide both sides by $11$ $11$ :

$\Rightarrow x > \frac{39}{11}$ $=> x > (39) / (11)$

Therefore, the solution to the inequality is $x > \frac{39}{11}$ $x > (39) / (11)$ .