Algebra.Com's Answer #755254 by ikleyn(53763)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "This problem wants you solve two inequalities separately\r\n" );
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document.write( " x + 2 < 5 (1)\r\n" );
document.write( "and\r\n" );
document.write( " x - 7 > -6 (2)\r\n" );
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document.write( "and then take the intersection of their sets of solutions.\r\n" );
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document.write( "It is the same as to solve the system of two inequalities \r\n" );
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document.write( "OK. So, our first step is to solve inequality (1). For it, subtract the number 2 from both sides. \r\n" );
document.write( "Inequality remains equivalent and takes the form\r\n" );
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document.write( " x < 5 - 2, \r\n" );
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document.write( "which is the same as\r\n" );
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document.write( " x < 3.\r\n" );
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document.write( "So, the set of solutions to the first inequality is { x < 3 }, or, in the interval notation ( , ).\r\n" );
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document.write( "Our next step is to solve inequality (2). For it, add the number 7 to both sides. \r\n" );
document.write( "Inequality remains equivalent and takes the form\r\n" );
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document.write( " x > -6 + 7, \r\n" );
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document.write( "which is the same as\r\n" );
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document.write( " x > 1.\r\n" );
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document.write( "Thus the set of solutions to this inequality is { x > 1 }, or, in the interval notation ( , ).\r\n" );
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document.write( "The intersection of the sets { x < 3 } and { x > 1} is the set { 1 < x < 3 }, or, in the interval notation, interval (1,3).\r\n" );
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document.write( "ANSWER. The solution of the problem is the set { 1 < x < 3 }, or, in the interval notation, interval (1,3).\r\n" );
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document.write( "Solved.\r
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document.write( "To find other similar solved problems, see the lesson \r
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document.write( " - Solving systems of linear inequalities in one unknown \r
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document.write( " - Solving compound inequalities \r
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document.write( "in this site.\r
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