document.write( "Question 121846: I need help solving the radical equation\r
\n" ); document.write( "\n" ); document.write( "2x+3-x+1=1 \n" ); document.write( "
Algebra.Com's Answer #89547 by bucky(2189)\"\" \"About 
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Several rules for solving equations such as these are:
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\n" ); document.write( "(1) Combine like terms on both sides
\n" ); document.write( "(2) Get the numbers on one side and the unknown variable terms on the other
\n" ); document.write( "(3) Combine terms again after they are collected on one side
\n" ); document.write( "(4) Divide by the multiplier of the unknown to solve
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\n" ); document.write( "Let's apply these rules to the given problem. You were given:
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\n" ); document.write( "2x + 3 - x + 1 = 1
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\n" ); document.write( "Let's apply rule (1) by combining like terms on the left side. Note the +3 and the +1 are like
\n" ); document.write( "terms and they add to give +4. Notice also that the 2x and -x are like terms and they combine
\n" ); document.write( "to +x. There is only a single term on the right side of the equation, so no combining is
\n" ); document.write( "needed on that side. So after applying rule (1) we are left with:
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\n" ); document.write( "x + 4 = 1
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\n" ); document.write( "Next apply rule (2). The variable term (in this problem it is x) is on the left side, but the
\n" ); document.write( "left side also has the constant 4. We need to get the +4 on the other side of the equation
\n" ); document.write( "so that it is not on the same side of the equal sign as the 1. You can do this by subtracting
\n" ); document.write( "+4 from both sides to get:
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\n" ); document.write( "x + 4 - 4 = 1 - 4
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\n" ); document.write( "Now apply rule (3) and combine the constants on both side. On the left side the +4 and the -4
\n" ); document.write( "combine to cancel each other out. So they drop from the equation. On the right side the +1
\n" ); document.write( "and the -4 combine to give -3. As a result of this combining the equation is reduced to:
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\n" ); document.write( "x = -3
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\n" ); document.write( "Finally, you apply rule (4). But in this problem the multiplier of x is just +1 and dividing
\n" ); document.write( "both sides of the equation by +1 changes nothing. So you have solved the problem, and the
\n" ); document.write( "answer you got was x = -3
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\n" ); document.write( "You can check this problem by returning to the original equation you were given and substituting
\n" ); document.write( "-3 for x to see if both sides of the equation are equal. The original equation was:
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\n" ); document.write( "2x + 3 - x + 1 = 1
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\n" ); document.write( "Putting -3 in for x results in:
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\n" ); document.write( "2(-3) + 3 - (-3) + 1 = 1
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\n" ); document.write( "This reduces to:
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\n" ); document.write( "-6 + 3 + 3 + 1 = 1
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\n" ); document.write( "If you algebraically add the numbers on the left side, the equation becomes:
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\n" ); document.write( "1 = 1
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\n" ); document.write( "And since this balances, we have the correct answer of x = -3.
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\n" ); document.write( "Hope this helps you to understand some fundamental processes of solving equations.
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