document.write( "Question 72678: If (a) does not equal (b), solve for x in terms of (a) and (b):
\n" ); document.write( "ax+b(ax-b)=a(bx-a)-bx \n" ); document.write( "

Algebra.Com's Answer #52040 by Earlsdon(6294) $\"\"$ $\"About$

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Solve for x:
\n" ); document.write( " $\"ax%2Bb%28ax-b%29+=+a%28bx-a%29-bx\"$ Expand the parentheses.
\n" ); document.write( " $\"ax%2Babx-b%5E2+=+abx-a%5E2-bx\"$ Simplify. Subtract abx from both sides.
\n" ); document.write( " $\"ax-b%5E2+=+-a%5E2-bx\"$ Add $\"a%5E2\"$ to both sides.
\n" ); document.write( " $\"a%5E2-b%5E2%2Bax+=+-bx\"$ Add bx to both sides.
\n" ); document.write( " $\"a%5E2-b%5E2%2Bax%2Bbx+=+0\"$ Simplify.
\n" ); document.write( " $\"%28a%5E2-b%5E2%29%2Bx%28a%2Bb%29+=+0\"$ Subtract $\"%28a%5E2-b%5E2%29\"$ from both sides.
\n" ); document.write( " $\"x%28a%2Bb%29+=+-%28a%5E2-b%5E2%29\"$ Divide both sides by $\"%28a%2Bb%29\"$
\n" ); document.write( " $\"x+=+-%28a%5E2-b%5E2%29%2F%28a%2Bb%29\"$ Factor the numerator.
\n" ); document.write( " $\"x+=+-%28%28a%2Bb%29%28a-b%29%29%2F%28a%2Bb%29\"$ Cancel the $\"%28a%2Bb%29\"$
\n" ); document.write( " $\"x+=+-%28a-b%29\"$
\n" ); document.write( " $\"x+=+b-a\"$
\n" ); document.write( " \n" ); document.write( "

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