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<h1>
EMSolution online - Math tests and fully explained step-by-step solutions - Algebra Inequalites
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Test - 3
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<b>1. Solve the inequality</b>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><msup><mi>t</mi><mi>4</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>11 </mi><msup><mi>t</mi><mi>3</mi></msup></mrow><mrow><mo>+</mo><mi>39 </mi><msup><mi>t</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>49 </mi><mi>t</mi></mrow><mrow><mo>+</mo><mi>20 </mi></mrow></mrow>
<mo>&#x003C;</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
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<b>2. Solve the inequality</b>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>16 </mi><msup><mi>s</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>4 </mi><mi>s</mi></mrow><mrow><mo>+</mo><mi>3 </mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mi>8 </mi><msup><mi>s</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>2 </mi><mi>s</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>7 </mi></mrow></mrow>
</mrow></mfrac></mrow>
<mo>+</mo>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>8 </mi><msup><mi>s</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>2 </mi><mi>s</mi></mrow><mrow><mo>+</mo><mi>5 </mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>16 </mi><msup><mi>s</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>4 </mi><mi>s</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>8 </mi></mrow></mrow>
</mrow></mfrac></mrow>
<mo>&#x003C;</mo>
<mrow><mrow><mfrac><mi>3</mi><mi>2</mi></mfrac></mrow></mrow>
</mrow>
</mrow>
</math>
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<b>3. Solve the inequality</b>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><msup><mi>s</mi><mi>3</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>6 </mi><msup><mi>s</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>12 </mi><mi>s</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>8 </mi></mrow></mrow>
<mo>-</mo>
<msup>
<mfenced><mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>3 </mi><mi>s</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>7 </mi></mrow></mrow>
</mrow></mfenced>
<mrow>
<mrow><mrow><mi>3 </mi></mrow></mrow>
</mrow></msup>
</mrow>
<mrow>
<mrow><mrow><mi>2 </mi><mi>s</mi></mrow><mrow><mo>+</mo><mi>5 </mi></mrow></mrow>
</mrow></mfrac></mrow>
<mo>+</mo>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>3 </mi><mi>s</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>8 </mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
<mo>&#x003E;</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
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<b>4. Solve the inequality</b>
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<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><msup><mi>z</mi><mi>4</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>8 </mi><msup><mi>z</mi><mi>3</mi></msup></mrow><mrow><mo>+</mo><mi>4 </mi><msup><mi>z</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>9 </mi><mi>z</mi></mrow><mrow><mo>+</mo><mi>2 </mi></mrow></mrow>
<mo>&#x2264;</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
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<b>5. Solve the inequality</b>
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<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mfrac>
<mrow>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>3 </mi><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>+</mo><mi>20 </mi><mi>y</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>25 </mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
<mo>&#x00B7;</mo>
<mrow><mo maxsize="2">(</mo><mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>y</mi></mrow><mrow><mo>+</mo><mi>7 </mi></mrow></mrow>
</mrow><mo maxsize="2">)</mo></mrow>
</mrow>
<mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>y</mi></mrow><mrow><mo>+</mo><mi>5 </mi></mrow></mrow>
</mrow></mfrac></mrow>
<mo>+</mo>
<mrow><mfrac>
<mrow>
<mrow><mrow><mo>&#x002D;&#x00A0;</mo><msup><mi>y</mi><mi>3</mi></msup></mrow><mrow><mo>+</mo><mi>18 </mi><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>105 </mi><mi>y</mi></mrow><mrow><mo>+</mo><mi>200 </mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><msup><mi>y</mi><mi>2</mi></msup></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>10 </mi><mi>y</mi></mrow><mrow><mo>+</mo><mi>25 </mi></mrow></mrow>
</mrow></mfrac></mrow>
<mo>&#x2264;</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
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