How do you solve -3/8(16x - 8) >4?

Sep 2, 2016

$x < - \frac{1}{6}$

Explanation:

Treat it the same as an equation, unless you multiply or divide by a negative, in which case the sign in the middle changes around.

I have used two methods. I thought the first would be quicker and easier - it wasn't.!!

Second method is much better.

Method 1 Isolate the bracket first.

$- \frac{3}{8} \left(16 x - 8\right) > 4 \leftarrow \text{ multiply by } - \frac{8}{3}$

$\textcolor{red}{- \frac{8}{3} \times} - \frac{3}{8} \left(16 x - 8\right) < 4 \textcolor{red}{\times - \frac{8}{3}} \text{ note} > \to <$

$16 x - 8 < - \frac{32}{3}$

$16 x < - \frac{32}{3} + 8$

$16 x < - \frac{8}{3}$

$x < - \frac{\cancel{8}}{3 \times {\cancel{16}}^{2}}$

$x < - \frac{1}{6}$

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Method 2 Remove the brackets with distributive law.

$- \frac{3}{8} \left(16 x - 8\right) > 4$

$- 6 x + 3 > 4$

$3 - 4 > 6 x$

$- 1 > 6 x$

$- \frac{1}{6} > x$

This is the same as $x < - \frac{1}{6}$