document.write( "Question 825884: Solve\r
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Algebra.Com's Answer #497675 by math-vortex(648) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "Solve for w.\r\n" );
document.write( "(w-3)/(w+2)=(6-w)/(w-12)\r\n" );
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document.write( "A SOLUTION:\r\n" );
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document.write( "I'll go step-by-step so you can see what's happening. Multiply both sides by (w+2). This will \r\n" );
document.write( "clear the denominator on left side,\r\n" );
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document.write( "Now multiply both sides by (w-12). This will clear denominator on the right side.\r\n" );
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document.write( "Now use the distributive property to multiply all the factors out to polynomial form.\r\n" );
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document.write( "Combine like terms and rearrange by descending degree on both sides.\r\n" );
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document.write( "This is a quadratic equation. We need to set it equal to zero to solve. Rewrite as an equivalent \r\n" );
document.write( "equation with all terms on the left.\r\n" );
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document.write( "I always try to factor first because it's faster than the quadratic formula.\r\n" );
document.write( "factors of 2w^2 are 2w and w.\r\n" );
document.write( "factors of 24 are positive/positive or negative/negative\r\n" );
document.write( "24 and 1, \r\n" );
document.write( "12 and 2, \r\n" );
document.write( "8 and 3,\r\n" );
document.write( "6 and 4\r\n" );
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document.write( "We want a combination that sums to -19x when we distribute. The factors -8 and -3 will\r\n" );
document.write( "work because (-8)(2x)+(-3(x)=-19x.\r\n" );
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document.write( "Write the quadratic equation in factored form.\r\n" );
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document.write( "By the Zero Product Property, either\r\n" );
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document.write( " OR \r\n" );
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document.write( "Therefore, our solutions are x = 1.5 or x = 8.\r\n" );
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document.write( "Check you work by substituting these values into the original equation.\r\n" );
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document.write( "For x = 8:\r\n" );
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document.write( " CHECK!\r\n" );
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document.write( "For x=1.5:\r\n" );
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document.write( " CHECK!\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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