document.write( "Question 65493: (64)A common mistake when solving equations is the following:
\n" ); document.write( " The equation: 2(x – 2) = x + 3
\n" ); document.write( " First step in solving: 2x – 2 = x + 3
\n" ); document.write( "Write a clear explanation of what error has been made. What could be done to avoid this error?\r
\n" ); document.write( "\n" ); document.write( "(92) Statistics. Sam must have an average of 70 or more in his summer course to obtain a grade of C. His first three test grades were 75,63, and 68. Write an inequality representing the score that Sam must get on the last test to get a C grade.\r
\n" ); document.write( "\n" ); document.write( "(94) Business and finance. The cost for a long-distance telephone call is $0.36 for the first minute and $0.21 for each additional minute or portion thereof. Write an inequality representing the number of minutes a person could talk without exceeding $3. \n" ); document.write( "
Algebra.Com's Answer #46035 by Edwin McCravy(20065)\"\" \"About 
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(64)A common mistake when solving equations is the following:\r\n" );
document.write( "The equation: 2(x – 2) = x + 3\r\n" );
document.write( "First step in solving: 2x – 2 = x + 3\r\n" );
document.write( "Write a clear explanation of what error has been made. \r\n" );
document.write( "What could be done to avoid this error?\r\n" );
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document.write( "If we have this equation, we must remove the parentheses\r\n" );
document.write( "by using the distributive principle\r\n" );
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document.write( "2(x - 2) = x + 3\r\n" );
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document.write( "The distributive principle says you must multiply the outer \r\n" );
document.write( "red 2 by both the blue x and the green -2, so that the first \r\n" );
document.write( "step in solving is\r\n" );
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document.write( "2x - 4 = x + 3\r\n" );
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document.write( "The mistake was forgetting to multiply the red 2 by the green -2.\r\n" );
document.write( "Nobody forgets to multiply the red 2 by the blue x, but then people\r\n" );
document.write( "get in a rush and forget to multiply the red 2 by the green -2, and\r\n" );
document.write( "they get\r\n" );
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document.write( "2x - 2 = x + 3\r\n" );
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document.write( "instead, which is wrong.\r\n" );
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document.write( "One way to avoid making this error is to get in the habit of drawing\r\n" );
document.write( "lines something like this to remind you that you must make BOTH\r\n" );
document.write( "multiplications, not just the first one only:\r\n" );
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document.write( "2(x – 2) = x + 3\r\n" );
document.write( "|____|\r\n" );
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document.write( "(92) Statistics. Sam must have an average of 70 or more in his summer\r\n" );
document.write( "course to obtain a grade of C. His first three test grades were \r\n" );
document.write( "75, 63, and 68. Write an inequality representing the score that Sam \r\n" );
document.write( "must get on the last test to get a C grade. \r\n" );
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document.write( "Let the fourth grade be x, then the average is found by adding up\r\n" );
document.write( "the four grades and dividing by 4, like this\r\n" );
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document.write( " 75 + 63 + 68 + x\r\n" );
document.write( "------------------  \r\n" );
document.write( "         4     \r\n" );
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document.write( "This must be greater than or equal to a 70 in order for Sam to make\r\n" );
document.write( "a C.  So we form the inequality\r\n" );
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document.write( " 75 + 63 + 68 + x\r\n" );
document.write( "------------------ > 70  \r\n" );
document.write( "         4\r\n" );
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document.write( "or\r\n" );
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document.write( " 206 + x\r\n" );
document.write( "--------- > 70  \r\n" );
document.write( "    4 \r\n" );
document.write( "         \r\n" );
document.write( "Then we multiply both sides of the inequality by 4 to clear of\r\n" );
document.write( "fractions.  The inequality symbol will not reverse because we\r\n" );
document.write( "are multiplying by a positive number 4.\r\n" );
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document.write( "206 + x > 280\r\n" );
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document.write( "Subtract 206 from both sides:\r\n" );
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document.write( "      x > 74\r\n" );
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document.write( "(94) Business and finance. The cost for a long-distance telephone call \r\n" );
document.write( "is $0.36 for the first minute and $0.21 for each additional minute or \r\n" );
document.write( "portion thereof. Write an inequality representing the number of \r\n" );
document.write( "minutes a person could talk without exceeding $3.\r\n" );
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document.write( "Let x = the number of minutes:\r\n" );
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document.write( "The first minute costs $0.36\r\n" );
document.write( "The remaining x-1 minutes cost $0.21 each\r\n" );
document.write( "So the remaining x-1 minutes altogether costs $0.21(x-1)\r\n" );
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document.write( "Total cost = $0.36 + $0.21(x-1) \r\n" );
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document.write( "This must be less than or equal $3.00. So we have:\r\n" );
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document.write( "$0.36 + $0.21(x-1) < $3.00\r\n" );
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document.write( "Multiply through by 100 and drop the $'s\r\n" );
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document.write( "36 + 21(x - 1) < 300\r\n" );
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document.write( " 12 + 7(x - 1) < 100 \r\n" );
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document.write( "   12 + 7x - 7 < 100 \r\n" );
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document.write( "        7x + 5 < 100\r\n" );
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document.write( "Subtract 5 from both sides\r\n" );
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document.write( "            7x < 95\r\n" );
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document.write( "Divide both sides by 7, which will not\r\n" );
document.write( "reverse the inequality symbol:\r\n" );
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document.write( "             x < 13.57142857\r\n" );
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document.write( "So the answer is really\r\n" );
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document.write( "             x < 13 minutes\r\n" );
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document.write( "which will be 36 cents for the first minute\r\n" );
document.write( "and 21 cents for the other 12 minutes, and\r\n" );
document.write( "will cost Sam $2.88.  However if Sam talks even\r\n" );
document.write( "one second more than 13 minutes, it will cost\r\n" );
document.write( "him another 21 cents. making the bill be\r\n" );
document.write( "$3.09 which exceeds $3.00\r\n" );
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document.write( "Edwin
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