document.write( "Question 1091097: Hi, I have the question 5n + 24 = |8 - 3n| for my homework and I've gotten -2 and -16 as the answers, but I don't know if that's correct or if it would only be -2 as the answer \n" ); document.write( "
Algebra.Com's Answer #705517 by ikleyn(52847)\"\" \"About 
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document.write( "1.  First of all, you can easily check if your numbers satisfy the equation.\r\n" );
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document.write( "    For n = -2 you have\r\n" );
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document.write( "    a)  left side is  5*(-2) + 24 = -10 + 24 = 14.\r\n" );
document.write( "    b)  right side is  |8 - 3*(*(-2)| = |8 + 6| = 14.\r\n" );
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document.write( "    So, n = -2 is the solution.\r\n" );
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document.write( "    For n = -16 you have \r\n" );
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document.write( "    a)  left side is  5*(-16) + 24 = -80 + 24 = -56.\r\n" );
document.write( "    b)  right side is  |8 - 3*(-16)| = |8 + 48| = 56.\r\n" );
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document.write( "    So, n = 16 is not the solution.\r\n" );
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document.write( "2.  The plots of the functions are shown below:\r\n" );
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document.write( "    \r\n" );
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document.write( "Plots y = 5x + 24 (red) and  y = |8 - 3x| (green)\r\n" );
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\n" ); document.write( "\n" ); document.write( "These plots (graphical solution) show you visually that there is only one solution.\r
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\n" ); document.write( "\n" ); document.write( "Surely, from the mathematical point of view, it is not the proof.
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document.write( "3.  Now I will show you how to solve this equation\r\n" );
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document.write( "    5n + 24 = |8 - 3n|.     (1)\r\n" );
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document.write( "    Looking into the right sde, you can notice that there is the critical point n = \"8%2F3\" = \"2\" \"2%2F3\".\r\n" );
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document.write( "     Case a)  If  n <= \"8%2F3\",  then 8 - 3n >= 0, and the right side of the equation (1) is 8-3n.\r\n" );
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document.write( "              Hence, in this case the equation (1) takes the form\r\n" );
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document.write( "              5n + 24 = 8 - 3n.    (2)\r\n" );
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document.write( "              Simplify it further and solve for n:\r\n" );
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document.write( "              5n + 3n = 8 - 24  ====>  8n = -16  ====>  n = -2.\r\n" );
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document.write( "              This value of n satisfy the inequality  n <= \"8%2F3\".\r\n" );
document.write( "              Hence,  n = -2  is the solution to (2)  and  is the solution to (1).\r\n" );
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document.write( "              Case a)  is completed.\r\n" );
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document.write( "     Case b)  If  n > \"8%2F3\",  then 8 - 3n < 0, and the right side of the equation (1) is 3n-8.\r\n" );
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document.write( "              Hence, in this case the equation (1) takes the form\r\n" );
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document.write( "              5n + 24 = 3n - 8.    (3)\r\n" );
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document.write( "              Simplify it further and solve for n:\r\n" );
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document.write( "              5n - 3n = -8 - 24  ====>  2n = -32  ====>  n = -16.\r\n" );
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document.write( "              But this value of n DOES NOT satisfy the inequality  n > \"8%2F3\".\r\n" );
document.write( "              Hence,  n = -16, alghough  is the solution to (3),  IS NOT the solution to (1).\r\n" );
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document.write( "              Case b)  is completed.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus we found that the only solution to the given equation  (1)  is   n= -2.\r
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\n" ); document.write( "\n" ); document.write( "        **************
\n" ); document.write( "        *** Solved ***
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\n" ); document.write( "\n" ); document.write( "To see more similar solved problems/  (your samples),  look into the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Absolute Value equations\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 1\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 2\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Linear Terms under the Absolute Value sign. Lesson 3\r
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\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Quadratic Terms under the Absolute Value sign. Lesson 1\r
\n" ); document.write( "\n" ); document.write( "    - HOW TO solve equations containing Quadratic Terms under the Absolute Value sign. Lesson 2 \r
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Absolute Value equations \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Read them attentively and become an expert in this area.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "\"Solving Absolute values equations\".\r
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