Points A, B and C are collinear with B between A and C. If AB=3x-4 and BC=4x+7 and AC=12x-12, find the value of x?
Make a sketch and you will see that
12x - 12 = 3x-4 + 4x + 7
easy to solve
To find the value of x, we need to use the fact that A, B, and C are collinear, which means that the sum of the lengths of any two segments within the line is equal to the length of the entire line segment.
In this case, we have AB + BC = AC.
Substituting the given values, we have:
3x - 4 + 4x + 7 = 12x - 12
Combine like terms:
7x + 3 = 12x - 12
Subtract 7x from both sides:
7x - 7x + 3 = 12x - 7x - 12
3 = 5x - 12
Add 12 to both sides:
3 + 12 = 5x - 12 + 12
15 = 5x
Divide both sides by 5:
15/5 = 5x/5
3 = x
Therefore, the value of x is 3.