document.write( "Question 1142337: Six times a number, x, increased by 4 is less than 2 or greater than 10. \n" ); document.write( "

Algebra.Com's Answer #763052 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "It is so called compound inequality\r\n" );
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document.write( "    6x + 4 < 2  OR  6x + 4 > 10.\r\n" );
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document.write( "Notice that the two inequalities are connected by the service word \" OR \".\r\n" );
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document.write( "It means that the solution is THE UNION  of the solution sets to each of the two participating inequalities.\r\n" );
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document.write( "For the first of the two inequalities the solution is  x <  = .\r\n" );
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document.write( "For the second inequality the solution is  x >  = 1.\r\n" );
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document.write( "So, the solution to the given compound inequality is the union of two sets\r\n" );
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document.write( "    { x | x <  }  U  { x | x > 1}.\r\n" );
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document.write( "In interval form, it is the union of two intervals   (,) U (1,oo).\r\n" );
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\n" ); document.write( "Comment from student : thank you so much. i have one more question \r
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\n" ); document.write( "\n" ); document.write( "Triple a number, x, increased by 1 is between -20 and 10. What are the solutions for x?
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\n" ); document.write( "\n" ); document.write( "My response : In Math, using words instead of mathematical symbols, often leads to ambiguity.\r
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\n" ); document.write( "\n" ); document.write( "In your case, these words \" is between -20 and 10 \" leave it unclear if the endpoints are included.\r
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\n" ); document.write( "\n" ); document.write( "Therefore, I will use the sign \" <= \" for certainty.\r
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document.write( "-20 <= 3x + 1 <= 10\r\n" );
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document.write( "Subtract  1 (one) from both sides. You will get an equivalent inequality\r\n" );
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document.write( "-20 - 1 <= 3x <= 10 - 1,   or\r\n" );
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document.write( "-21 <= 3x < 9.\r\n" );
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document.write( "Now divide all three terms of the last inequality by 3. You will get\r\n" );
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document.write( "-7 <= x <= 3.\r\n" );
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document.write( "It is your ANSWER :  -7 <= x <= 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For inequalities, see introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Solving simple and simplest linear inequalities \r
\n" ); document.write( "\n" ); document.write( "    - Solving systems of linear inequalities in one unknown \r
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\n" ); document.write( "\n" ); document.write( "Consider them as your textbook, handbook, guide, tutorial and (free of charge) home teacher.\r
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\n" ); document.write( "\n" ); document.write( "Learn the subject from there once and for all.\r
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\n" ); document.write( "\n" ); document.write( "Happy learning !\r
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