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<title>A.I.15.37</title>
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<div class="feladat">
<b>Feladat: 15.37.</b><br /> <a name="algI_GHP_356" />[<a href="bib_box.php?mode=sneh--j-&amp;citation_num=65" target="bib_box" onclick="mutat('bib_box.php?mode=sneh--j-&amp;citation_num=65'); return false;">65</a>] Oldjuk meg az alábbi egyenlőtlenségeket!

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<br /><b>a)</b> <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:mfrac><m:mrow><m:mn>7</m:mn><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>3</m:mn></m:mrow>

<m:mrow><m:mn>4</m:mn><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>2</m:mn></m:mrow>

</m:mfrac>

<m:mi>&ensp;</m:mi><m:mo>&gt;</m:mo><m:mi>&ensp;</m:mi><m:mn>0</m:mn></m:mrow></m:math>;<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br />

<b>b)</b> <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:mfrac><m:mrow><m:mn>7</m:mn><m:mi>x</m:mi><m:mo>+</m:mo><m:mn>3</m:mn></m:mrow>

<m:mrow><m:mn>4</m:mn><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>2</m:mn></m:mrow>

</m:mfrac>

<m:mi>&ensp;</m:mi><m:mo>&lt;</m:mo><m:mi>&ensp;</m:mi><m:mn>2</m:mn></m:mrow></m:math>;<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br /><b>c)</b>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:mfrac><m:mrow><m:mn>3</m:mn><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>8</m:mn></m:mrow>

<m:mrow><m:mn>5</m:mn><m:mo>-</m:mo><m:mi>x</m:mi></m:mrow>

</m:mfrac>

<m:mi>&ensp;</m:mi><m:mo>&ge;</m:mo><m:mi>&ensp;</m:mi><m:mn>2</m:mn></m:mrow></m:math>;<br /><m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mi>&ensp;</m:mi></m:mrow></m:math><br /><b>d)</b>

<m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow>

<m:mfrac><m:mrow><m:mn>3</m:mn><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo></m:mrow>

<m:mrow><m:mn>2</m:mn><m:mo stretchy="false">(</m:mo><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>3</m:mn><m:mo stretchy="false">)</m:mo></m:mrow>

</m:mfrac>

<m:mi>&ensp;</m:mi><m:mo>&lt;</m:mo><m:mi>&ensp;</m:mi>

<m:mfrac><m:mrow><m:mn>4</m:mn><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>7</m:mn></m:mrow>

<m:mrow><m:mi>x</m:mi><m:mo>-</m:mo><m:mn>3</m:mn></m:mrow>

</m:mfrac>

</m:mrow></m:math>.<br />
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<div class="feladat">
<a name="_hint_algI_GHP_356" /><b>Segítség, útmutatás: 15.37</b><br />
A b) feladatban érdemes úgy rendezni, hogy az egyik oldalon <m:math xmlns="http://www.w3.org/1998/Math/MathML">

<m:mrow><m:mn>0</m:mn></m:mrow></m:math>

álljon, mert úgy közös nevezőre hozás után az a) feladattal azonos

nehézségűvé válik a probléma.
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