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HELP ME SOLVE FOR X 3X-7=3(X + 1) PROBLEM 2 -5( X - 1) + 4( 2x - 3) = -2(X + 2) -8

I had 33 problems to solve by in the morning, out of 33 problems these two have been a big problem can you help me solve by showing me how you get the solution and not just the answer....

last question:  a standard rectangular highway billboard sign has a perimeter of 120 feet. The length is 6 more than twice the width. Find the width of the sign? 

 

can someone please help me so I can go to sleep

 

Janice

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3 Answers

a standard rectangular highway billboard sign has a perimeter of 120 feet. The length is 6 more than twice the width. Find the width of the sign?

Let w = width

then

2w+6 = length

2(w + 2w+6) = 120

w + 2w+6 = 60

3w+6 = 60

3w = 54

w = 18 feet (width)

This is an algebra problem. To set it up, first analyze the numbers and try to create a diagram of the situation.

Let's first label the length L, and width W. It says that the length is 6 [feet] more than twice the width, which allows you to set up this equation:


L = 2W + 6

We also know that the perimeter (the distance around the billboard) is 120 feet. Being the sum of all sides, we can express the perimeter like so:


P = 2W + 2L = 120.


Now this is a system of equations which we can solve. I would recommend first solving for 2W, since that appears in both equations. Using the second equation, it follows:

2W = 120 - 2L


Now, substitute this back into the first equation:

L = 2W + 6 = 120 - 2L + 6 = 126 - 2L, or written more simply: L = 126 - 2L

Now solve for L:

3L = 126 --> L = 42 [feet]

But since the question asked for width, let's plug this value back into either equation and solve for W. I'll use the first:

L = 2W + 6

W = (L - 6)/2 = (42 - 6)/2 = 36/2 = 18 [feet]

so the width of the billboard is 18 feet!

 

Good night. :)

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

XXX-XXXX

120 = 120 checked!

Comments

Kevin you have been a life saver tonight....I will be speaker with my professor in the morning because I like the way you explain the solution most just return the answer only, what good is that to me if I don't know how to do the work..I can understand it better this way because you walk me through the process..thank you I will be intouch real soon like Tommorow, soon as I research the site during study hall

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