Problem 1: 3x  7 = 3 (x+1)
Distribute to get
3x  7 = 3x + 1
Subtract 3x from both sides, and you're left with
7 = 1
Now, we know that 7 does NOT equal 1, so there is NO SOLUTION to this equation.
Problem 2: 5( X  1) + 4( 2x  3) = 2(X + 2) 8
Again, distribute:
(5)(x) + (5)(1) + (4)(2x) + (4)(3) = (2)(x) + (2)(2)  8
Simplify:
5x + 5 + 8x  12 = 2x 4  8
Collect like terms and simplify:
3x  7 = 2x  12
5x = 5
x = 1
Billboard Problem:
We know that the perimeter of a rectangle is twice the length plus twice the width. Using what we know, we get
2l + 2w = 120 feet
The problem also tells us that the length is 6 more than twice the width. This tells us
l = 6 + 2w
We can then put the second equation in for l in the first, and get
2 (6 + 2w) + 2w = 120
Simplify
12 + 4w + 2w = 120
12 + 6w = 120
6w = 108
w = 18 feet. <==== What we need
We can find the length with l = 2w + 6 = 2 (18) + 6 = 42 feet
And check ourselves by plugging length and width into the first equation
2 (42) + 2 (18) = 120
XXXXXXX
120 = 120 checked!
1/16/2013

Kevin S.
Comments
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