if bc = 2x-3 and ac = 2x+10, find the length of ab

To find the length of AB, we need to use the given equations and apply the properties of triangles.

Let's consider the triangle ABC.

Given: BC = 2x - 3 and AC = 2x + 10.

We are looking for the length of AB.

In a triangle, the sum of the lengths of any two sides is always greater than the length of the third side.

So we can write the following inequalities:

AB + BC > AC (1)
AB + AC > BC (2)
BC + AC > AB (3)

Now let's solve these inequalities to find the possible range of values for AB.

From equation (1):
AB + (2x - 3) > (2x + 10)
AB > 13

From equation (2):
AB + (2x + 10) > (2x - 3)
AB > -13

From equation (3):
(2x - 3) + (2x + 10) > AB
4x + 7 > AB

Combining the inequalities, we can conclude that:
AB > 13 and AB > -13

Therefore, the length of AB is greater than 13.

However, we don't have enough information to determine the exact length of AB without knowing the value of x.

(2x+10) - (2x-3) = 7