Rovnica s absolútnou hodnotou
Rieš v danej množine rovnicu:\( \left| {2 x + 6} \right|\ -\ \left| {4\ –\ 2 x} \right| + \left| {x + 7} \right| = 4 \) v \( \normalsize\left\langle-2;2\right) \)
\( \left| {2 x + 6} \right|\ –\ \left| {4\ –\ 2 x} \right| + \left| {x + 7} \right| = 4 \)
\( 2 x + 6\ –\ \left( {4\ –\ 2 x} \right) + x + 7 = 4 \)
\( 2 x + 6\ –\ 4 + 2 x + x + 7 = 4 \)
\( 5 x =\ – 5\ \ \ \ \ /:5 \)
\( x =\ – 1 \)
\( \normalsize K=\left\{{-1}\right\} \)
\( \left| {2 x + 6} \right|\ –\ \left| {4\ –\ 2 x} \right| + \left| {x + 7} \right| = 4 \)
\( 2 x + 6\ –\ \left( {4\ –\ 2 x} \right) + x + 7 = 4 \)
\( 2 x + 6\ –\ 4 + 2 x + x + 7 = 4 \)
\( 5 x =\ – 9\ \ \ \ \ /:5 \)
\( x =\ – 1.8 \)
\( \normalsize K=\left\{{-1.8}\right\} \)
\( \left| {2 x + 6} \right|\ –\ \left| {4\ –\ 2 x} \right| + \left| {x + 7} \right| = 4 \)
\( 2 x + 6\ –\ \left( {4\ –\ 2 x} \right) + x + 7 = 4 \)
\( 2 x + 6\ –\ 4 + 2 x + x + 7 = 4 \)
\( 5 x =\ – 7\ \ \ \ \ /:5 \)
\( x =\ – 1.4 \)
\( \normalsize K=\left\{{-1.4}\right\} \)
\( \left| {2 x + 6} \right|\ –\ \left| {4\ –\ 2 x} \right| + \left| {x + 7} \right| = 4 \)
\( 2 x + 6\ –\ \left( {4\ –\ 2 x} \right) + x + 7 = 4 \)
\( 2 x + 6\ –\ 4 + 2 x + x + 7 = 4 \)
\( 5 x =\ – 3\ \ \ \ \ /:5 \)
\( x =\ – 0.6 \)
\( \normalsize K=\left\{{-0.6}\right\} \)