Equations

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/