Help PLeez! Um simple Algebra!?

Question

How do you solve this:

3 ( x + 1) = 2 ( x + 11)

- I know to use the distrubuting prop. but after the 2nd step I get confused,pleez help!


The length of a rectangle is 5 cm greater than it's width. The perimeter is 58 cm. Find the dimensions of the rectangle.

~thankz!

Answer 1

3x+3= 2x +22
-3 -3
3x=2x+19
-2x -2x
x=19



2(x+5)+ 2(x)= 58
2x+10+2x=58
4x+10= 58
-10 -10
4x=48
divide by 4
x=12

Answer 2

3(x + 1) = 2(x + 11)
3x + 3 = 2(x + 11) Distribute the 3
3x + 3 = 2x + 22 Distribute the 2
x + 3 = 22 Subtract 2x from both sides
x = 19 Subtract 3 from both sides

Let the width of the rectangle be x. Then the length is x + 5. The perimeter is the sum of the sides, so
x + x + (x + 5) + (x + 5) = 58
4x + 10 = 58 Combine like terms
4x = 48 Subtract 10 from both sides
x = 12 Divide both sides by 4
That means the width is 12 cm and the length is 17 cm.

Answer 3

Hey there!

Here's the first answer.

3(x+1)=2(x+11) --> Write the problem.
3x+3=2x+22 --> Distribute 3 into x+1 and distribute 2 into x+11.
x+3=22 --> Subtract 2x on both sides of the equation.
x=19 Subtract 3 on both sides of the equation.

So the answer is x=19.

For the second problem, let l be the length, w be the width and P be the perimeter.

P=2(l+w) --> Write the perimeter of a rectangle formula.
58=2(l+w) --> Substitute 58 for P.
29=l+w --> Divide 2 on both sides of the equation.
29=(w+5)+w --> Substitute w+5 for l.
29=w+w+5 --> Gather the w terms together and the constant terms together.
24=w+w --> Subtract 5 on both sides of the equation.
24=2w --> Add w and w.
12=w --> Divide 2 on both sides of the equation.
w=12 --> Use symmetric property of equality i.e. if a=b, then b=a.
l=w+5 --> Write the second equation.
l=12+5 --> Substitute 12 for w.
l=17 Add 12 and 5.

So the length of the rectangle is 17 cm. and the width of the rectangle is 12 cm.

Hope it helps!

Answer 4

1) 3x+3=2x+22 U just try 2 keep the x's on 1 side and the plain #'s on the other.Once they cross the = sign u hav 2 do it's opposite.

3x-2x=22-3
x=19

2) 2(x)+2(x+5)=58

The 1st # has to travel when u see ( )U have to apply the whole equation inside.For example for the 2(x+5) part it's like the 2 is jumping to the x..=2x. Then it's jumping to the 5...=10.Now copy how u did the distributive property above because you will learn bettter that way.U can also Google the definition of perimeter and they'll tell u too. E-mail me if u don't get the distributive prop. and I'll explain it further. Good luck!It's really tricky at first for a lot of students but u'll get it. Good luck!

Answer 5

Distribute through to get 3x+3=2x+22.

Now you want to isolate the variable all on one side. Subtract 2x from each side. 3x+3-2x=2x+22-2x This will give you x+3=22.

Now all you have to do is subtract 3 from each side.
x+3-3=22-3 and this will give you x=19.

Now, if you go back into the original equation and substitute 19 in for the variable x...you will discover that it works.

Hope this helped.

Now for the second problem...Since rectangles have two sets of congruent sides, and you know that one of those sets is 5 cm longer than the other, you can set up your variables as x for on set of sides and x+5 as the other set.

Now you can do 2x + 2(x+5) = 58 since you know that the perimeter is the sum of all 4 sides on a rectangle.

Now distribute through: 2x + 2x + 10 = 58.

Simplify: 4x + 10 = 58

Subtranct 10 from each side: 4x = 48

Divide each side by 4: x = 12

Answer 6

Distribute through on both sides:
3(x+1)=2(x+11)
3x+3=2x+22

Put the x's on one side and the numbers on the other by subtracting 2x and 3 from each side:
3x-2x+3-3=2x-2x+22-3
x=19

-----
Put the words into equations

Length = Width +5 cm

Define perimeter in terms of length and width
Perimeter = 2L + 2W

Substitute and solve:
2(W+5)+2W=58
4W+10=58
4W=48
W=12
L=17
17+17+12+12=58 (checks)

Hope that helps.

Answer 7

Distribute to get:
3x + 3 = 2x + 22
Subtract 3 from both sides:
3x = 2x + 19
Subtract 2x from both sides:
x = 19


2. Length = Width + 5
Length + Length + Width + Width = 58
So... (W+5) + (W+5) + W + W = 58
4W + 10 = 58
4W = 48
W = 12
L = W + 5 = 12 + 5 = 17

Width = 12, Length = 17

Answer 8

3(x+1) = 2(x +11)
3x +3 = 2x +22
Now, you want to get all the Xs on one side of the equals sign. What ever you do to one side you MUST do the same to the other side. This will keep things equal. To get the 2x from the right side to the left side, you must subtract it from both sides of the equals sign.
3x -2x + 3 = 22
Now that you have all the Xs on one side of the equals sign, you want them to be all by themselves on one side of the equals sign. So, in this case, you must subtract 3 from both sides of the equals sign.
3x-2x=22-3
At this point you just perform the the obvious subtractions.
X=19

Length of rectangle = 5 + W
A perimeter is the sum of all of the sides of a rectangle. 58 = 2L + 2W
58 = 2(5+W) + 2W
I think the above equation is correct, but it's been a while since I've done a word problem.

Answer 9

First, multiply the outside numbers with everything inside the brackets.

3x + 3 = 2x +22

switch sides, and make opposite +/-

3x -2x = 22-3
x = 19

As for the second question:

Lx2 + Wx2 = 58
L=W+5

Therefore we can put the 2nd equation into the first.

(W+5) x 2 + Wx2 = 58
2w + 10 + 2w = 58
4w = 48
W = 12cm

Since the length is 2 times the width, the length is 24 while the width is 12.

Answer 10

3*(x+1) = 2*(x+11)
3*x+3 = 2x+22
Subtract 3 from both sides. Equality is still maintained.
3*x = 2*x +19
Subtract 2*x from both sides and get
x = 19. ANSWER

58 = 2*W + 2*L
L=W+5 Substitute this in equation above.
58=2*W + 2*(W+5)
58= 2*W + 2*W + 10
W=12
L=17
58=24+34=58 Check.

Answer 11

x = 19
rectangle = 12 cm by 17 cm 2(12)+2(17) = 58