document.write( "Question 482393: Simplifying by collecting like terms: I have a math problem that reads: Subtract the sum of -3m and -6p from their difference. My teacher says the answer is -12p. I am having trouble understanding the wording and setting up the problem. Can you help me solve this?
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Algebra.Com's Answer #330254 by kingme18(98) $\"\"$ $\"About$

You can put this solution on YOUR website!
This is definitely interesting wording!\r
\n" ); document.write( "\n" ); document.write( "Your problem: subtract the sum of -3m and -6p from their difference.\r
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\n" ); document.write( "\n" ); document.write( "Since the first thing it says is subtract, we know we're going to have to subtract two things. One of these is \"the sum of -3m and -6p\". \"Sum\" means add, so that means $\"%28-3m%29+%2B+%28-6p%29\"$ , or if you prefer, $\"-3m-6p\"$ . The other thing is their difference, which means subtraction. The difference of -3m and -6p is $\"%28-3m%29+-+%28-6p%29\"$ ; recall that a double negative (minus a negative) is the same as a positive, so $\"%28-3m%29+-+%28-6p%29\"$ is the same as $\"-3m+%2B+6p\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now we've dealt with \"the sum of -3m and -6p\" and \"their difference\". Last, we need to subtract the first thing FROM the second thing; that means we need to rearrange those groups. As an example: if I say \"subtract 3 from 5\", you'll do 5-3=2, not 3-5=-2. So we'll rearrange... Instead of the order the question puts it in (sum - difference), we'll flip. Thus, we'll do difference from above (simplified: $\"-3m%2B6p\"$ ) - sum from above (simplified: $\"-3m-6p\"$ ): $\"%28-3m%2B6p%29-%28-3m-6p%29\"$ . I used parentheses there because we need to distribute the subtraction: $\"-3m%2B6p%2B3m%2B6p\"$ . The -3m and 3m cancel, and $\"6p+%2B+6p+=+12p\"$ . Your answer is 12p.\r
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\n" ); document.write( "\n" ); document.write( "I talked to another math teacher, who agrees that this is 12p, not -12p. My guess is that your teacher didn't rearrange when subtracting (again, subtracting FROM something means to switch the order). \n" ); document.write( "

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