Tentukan himpunan penyelesasian dari soal-soal berikut ini : 1. 4x²+9x.... Question from @rahmatlubis

October 2018 1 21 Report

Tentukan himpunan penyelesasian dari soal-soal berikut ini :
1. 4x²+9x<9
2. |3x+4|<8
3. |2x-7|>3

izharulhaq78 $1.$
$4x^2+9x\ \textless \ 9\\4x^2+9x-9\ \textless \ 0\\4x^2+12x-3x-9\ \textless \ 0\\4x(x+3)-3(x+3)\ \textless \ 0\\(4x-3)(x+3)\ \textless \ 0\\\\4x-3\ \textless \ 0\\4x\ \textless \ 3\\x\ \textless \ \frac{3}{4}\\\\\text{atau}\\\\x+3\ \textless \ 0\\x\ \textless \ -3$

$\text{garis bilangan}\\\\\xrightarrow{---~~~+++~~---}\\{~~~~-3~~~~~~\frac{3}{4}}\\\\\boxed{HP=\{x|-3\ \textless \ x\ \textless \ \frac{3}{4}\}}$

$2.$
$|3x+4|\ \textless \ 8\\-8\ \textless \ 3x+4\ \textless \ 8\\\\-8\ \textless \ 3x+4\\-8-4\ \textless \ 3x\\-12\ \textless \ 3x\\-4\ \textless \ x\\\\3x+4\ \textless \ 8\\3x\ \textless \ 8-4\\3x\ \textless \ 4\\x\ \textless \ \frac{4}{3}\\\\\boxed{HP=\{x|-4\ \textless \ x\ \textless \ \frac{4}{3}\}}$

$3.$
$|2x-7|\ \textgreater \ 3\\2x-7\ \textless \ -3\text{ atau }2x-7\ \textgreater \ 3\\\\2x-7\ \textless \ -3\\2x\ \textless \ -3+7\\2x\ \textless \ 4\\x\ \textless \ 2\\\\2x-7\ \textgreater \ 3\\2x\ \textgreater \ 3+7\\2x\ \textgreater \ 10\\x\ \textgreater \ 5\\\\\boxed{HP=\{x|x\ \textless \ 2\text{ atau }x\ \textgreater \ 5\}}$

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