Simple geometry question?

Question

a. Find x if AC = 3x - 1 and BC = 12 - x.

b. Use the answer for x to find the value of AB.

I want explanation not just answer please and thank you =)

Answer 1

a. AC = BC
because C is the midpoint of AB
therefore,
3x - 1 = 12 - x
add x and 1 to both sides
3x + x = 1 + 12
simplify
4x = 13
divide both sides by 4
x = 13/4

b. since 3x - 1 = 12 - x
3x - 1 + 12 - x = AB
plug in 13/4 for x
3(13/4) - 1 + 12 - 13/4 = AB
39/4 - 1 + 12 - 13/4 = AB

since 4/4 = 1
and 48/4 = 12
substitute 4/4 for 1 and 48/4 for 12 into the equation so the all of the fractions have common denominators

39/4 - 4/4 + 48/4 - 13/4 = AB
keep PEMDAS in mind
35/4 + 48/4 - 13/4 = AB
83/4 - 13/4 = AB
70/4 = AB

Answer 2

This needs a diagram. Are A,B,C colinear? Is ABC a triangle? You need information that gives a relationship between AC and BC. If they are equal sides of an isosceles triangle, then

3x - 1 = 12 - x
4x = 13
x = 13/4

If C were the midpoint of AB, then after the above you could do

AC + BC = AB
3x - 1 + 12 - x = AB
2x + 11 = AB

and then 2(13/4) + 11 = 13/2 + 22/2 = 35/2 = 17.5 = AB

Answer 3

AC = 3x - 1 and BC = 12 - x.
AC - BC = (3x - 1) - 12- x =
2x - 13 =
2x = 13
x = 6,5

AC = 3(6.5 - 1) =
AC = 19,5 - 1 = 18.5

BC = 12 - 6.5 =
BC = 5.5

AB = AC - BC
AB = 18.5 - 5.5
AB = 13
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Answer 4

There is not enough information to solve the problem. How are A, B, and C related to each other? Are they vertices of a triangle? Points on a line? What? Be specific.

Answer 5

I am guessing that ABC is a triangle. You need to either give us an angle or (More likely) tell us which of the corners is a right angle?

Answer 6

we need to know the angles invloved.