Question

K is the midpoint of AB if AK =3x-4, and KB= 1/2x+6 find the length of AB

Answer 1

Is there any figure or diagram for this question
?

Answer 2

Set the length of AK equal to the length of KB and solve for x.
Then substitute x into 3x - 4 to find the length of AK.
Then multiply it by 2 to find the length of AB.

Answer 3

can you help me do that, ive been out of school for a while im not quite sure how to do any of this

Answer 4

Well if you know that k is the midpoint then you know that AK is equal to KB. Why because taht is teh defintion of midpoint; A midpoint divides something in equal pieces. So set AK=KB and solve for x
So
3x-4=1/2x+6...
Once you solve for x. Plug in x for AK+KB cause AK+KB=AB and that is what you want. Does that make sense?

Answer 5

yes i just dont know how to solve for x

Answer 6

Ok wellc solving for x is basic algebra. Your goal is to get the x by itself on one side and the numbers on the other side.. So what we do is
3x-4=1/2x+6 (I want to get x's on left side and numbers on left side)
So add 4 to both sides
3x=1/2x+10 Then subtract 1/2x to both sides
1.5x=10 N0w to get rid of the 1.5 Divide by 1.5 to both sides...
x=6 2/3

Answer 7

so the equation would be 3(6 2/3)-4=1/2(6 2/3)+6?

Answer 8

Plug in x for AK+KB cause AK+KB=AB and that is what you want. Not AK=KB we want to add them not set them equal to each other

Answer 9

ok so them added together is 25.1 is that my answer?

Answer 10

@Gerardo_cast23

Ok wellc solving for x is basic algebra. Your goal is to get the x by itself on one side and the numbers on the other side.. So what we do is
3x-4=1/2x+6 (I want to get x's on left side and numbers on left side)
So add 4 to both sides
3x=1/2x+10 Then subtract 1/2x to both sides
1.5x=10 N0w to get rid of the 1.5 Divide by 1.5 to both sides...

^^^^^^^^^^^^^^^^^^^^^^^
Careful with your arithmetic: 3x - (1/2)x = 3x - 0.5x = 2.5x, not 1.5 x.
x = 4, not x = 6 2/3

x=6 2/3

Answer 11

Oh oops sorry>.<

Answer 12

3x - 4 = (1/2)x + 6

Replace 1/2 with 0.5

3x - 4 = 0.5x + 6

Subtract 0.5x from both sides:

2.5x - 4 = 6

Add 4 to both sides:

2.5x = 10

Divide both sides by 2.5

x = 4

Answer 13

Now that we know x = 4, we can find AK:

AK = 3x - 4
AK = 3(4) - 4
AK = 12 - 4
AK = 8

Since AB = 2(AK)
AB = 2(8)
AB = 16

Answer 14

so my answer is 16?

Answer 15

Correct.

Answer 16

Thank you for checking/finding my mistake

Answer 17

ok thank you guys!

Answer 18

You're welcome. Good explanation, Gerardo. Anyone can make a silly mistake. I've made plenty of them. :-)