Question

If point C is between points A and B, AB=43, AC= -12x-9, BC= 24x+4, what is the value of X?

Answer 1

This problem is about the sum of segments, we just need to understand how to add all of them.

Notice that the segment AB is formed by the sum of AC and CB, as an equation it would be

$AB=AC+CB$

We know by given that AC=-12x-9, BC=24x+4, and AB=43. Using all these expressions, we have

$43=-12x-9+24x+4$

As you can observe, now we have a linear equation. First, we need to place all terms with a variable on the left side of the equation, and all terms without variables on the right side

$43+9-4=24x-12x$

Now, we solve each operation

$12x=48$

Finally, we divide each part by 12

$\frac{12x}{12}=\frac{48}{12}$

Therefore, the value of x is

$x=4$