Date: 5/24/96 at 9:28:45 From: Sarah Subject: Equations I'm having some trouble with a few equations: a) 7(4y+69)-8(2y-3) = 5(3y+7) b) (2x-5)(3x+2) = (6x+1)(x-7) c) (3x-2)(3x+2)+(x+4)(x-5) = (5x-1)(2x-3) It would be greatly appreciated if you could help me out. Sincerely, Sarah
Date: 5/24/96 at 10:17:22 From: Doctor Ethan Subject: Re: Equations and inequalities Hey Sarah, Let's see what we can do. I assume that your goal is to solve each equation for the variable. I will work through a) and b) and then I will let you see if you can follow my example on c). a) 7(4y + 69) - 8(2y - 3) = 5(3y + 7) Step one: Simplify each side. To do this we first (a) eliminate the parentheses by distribution and then (b) add up the sides. Step two: Combine like terms Now let's do the steps: 7(4y + 69) - 8(2y - 3) = 5(3y + 7) 1(a) Get rid of parentheses 28y + 483 - 16y + 24 = 8y + 35 1(b) Add up sides 12y + 507 = 8y + 35 2 Combine like terms 12y - 8y = 35 - 507 4y = -472 So y = 118. Now the second one: b) (2x-5)(3x+2) = (6x+1)(x-7) 1(a) Note: to do this step this time we will need to multiply two binomials. Do you know how to do this? I hope so. If not, write back for help with multiplying binomials. (Also x^2 means x squared.) So after step 1(a) we have 6x^2 -11x - 10 = 6x^2 - 41x - 7 (That was the big step - if you don't understand it, write back.) Okay. Now this time there is no part 1(b) and the sides are as added up as they're going to be, so we go stright to 2, and we bring all the x's to the lefthand side to get 6x^2 - 11x - 6x^2 + 41x = -7 + 10 Combining the terms we have 30x = 3 So x = 1/10 or .1 Hope this helps you out. Good luck on part c). -Doctor Ethan, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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