document.write( "Question 832402: Solve for y.
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Algebra.Com's Answer #502039 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 y. \r\n" );
document.write( "-4y + 10 = -2(3y + 1)\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "We want to write a series of equivalent equations using the properties of equality to get this equation in\r\n" );
document.write( "a \"y equals something\" form.\r\n" );
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document.write( "First, use the distributive property to clear the parentheses. We multiply -2 by each term in the \r\n" );
document.write( "parentheses.\r\n" );
document.write( "-4y + 10 = -2(3y + 1)\r\n" );
document.write( "-4y + 10 = -6y - 2\r\n" );
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document.write( "We would like all the terms on the left hand side, so add 6y to both sides. \r\n" );
document.write( "-4y + 10 + 6y = -6y - 2 + 6y\r\n" );
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document.write( "Combine the y-terms on each side. On the left, -4y+6y is 2y. On the right -6y+6y is 0.\r\n" );
document.write( "2y + 10 = -2\r\n" );
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document.write( "We want all the constant terms on the right hand side, so we subtract 10 from both sides.\r\n" );
document.write( "2y + 10 - 10 = -2 - 10\r\n" );
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document.write( "Combine like terms on each side. On the left, 10-10 is 0. On the right -2-10 is -12.\r\n" );
document.write( "2y = -12\r\n" );
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document.write( "We know the 2 times y equals -12. We want to know what y equals, so we divide each side by 2.\r\n" );
document.write( "2y/2 = -12/2\r\n" );
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document.write( "Simplify. On the left, 2y divided by 2 is y. On the right, -12/2 is -6.\r\n" );
document.write( "y = -6\r\n" );
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document.write( "It is a good habit to check you work by substituting -6 for y in the original equation.\r\n" );
document.write( "-4y + 10 = -2(3y + 1)\r\n" );
document.write( "-4(-6) + 10 = -2(3(-6) + 1)\r\n" );
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document.write( "Simplify.\r\n" );
document.write( "On the left, we have -4(-6) is 24. On the right, inside the parentheses, 3(-6) is -18.\r\n" );
document.write( "24 + 10 = -2(-18 + 1)\r\n" );
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document.write( "On the left, 24+10 is 34. On the right, inside the parentheses, -18+1 is -17.\r\n" );
document.write( "34 = -2(-17).\r\n" );
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document.write( "On the right, -2(-17) is 34.\r\n" );
document.write( "34 = 34.\r\n" );
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document.write( "When you check your work, this how you want things to work out...a number equal to the same number.\r\n" );
document.write( "This tells us that when y = -6, both sides of the equation have the same value,so the equation is true.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have ANY questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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