Given b is the midpoint of AC. AB=6x+7 and BC is 18x-4 what is the length of AB BC AC

Sinve b is midpoint of ac then ab and ac are the same length. So, 6x+7 = 18x-4.

Hope this helps.

Then what do I do with 6x+7 = 18x-4

Uh, solve to see what x is. Then use that value to evaluate AB and BC. They should come out the same.

If you're taking geometry, a little algebra I should be no problem...

To find the lengths of AB, BC, and AC, we need to use the given information that b is the midpoint of AC. The midpoint of a line segment is the point that divides the segment into two equal parts.

Let's set up the equation using the midpoint formula:

Midpoint formula: (x₁ + x₂)/2, (y₁ + y₂)/2

In this case, we'll use the x-coordinate of the midpoint, b, to find the lengths of AB and BC.

Since b is the midpoint of AC, we have the following equation:

AB + BC = 2 * b

Substituting the given values, AB = 6x + 7 and BC = 18x - 4:

(6x + 7) + (18x - 4) = 2 * b

Now we can solve this equation to find the value of x. Once we have the value of x, we can substitute it back into the equations AB = 6x + 7 and BC = 18x - 4 to find the lengths of AB, BC, and AC.

Solving the equation:

Combine like terms: 24x + 3 = 2 * b

Divide both sides of the equation by 2 to solve for b:

12x + 3 = b

Now we have an equation for b in terms of x.

To find the length of AB, substitute b = 12x + 3 into the equation AB = 6x + 7:

AB = 6x + 7
AB = 6x + 7
AB = 6(12x + 3) + 7
AB = 72x + 18 + 7
AB = 72x + 25

Similarly, to find the length of BC, substitute b = 12x + 3 into the equation BC = 18x - 4:

BC = 18x - 4
BC = 18(12x + 3) - 4
BC = 216x + 54 - 4
BC = 216x + 50

Finally, to find the length of AC, we can add AB and BC:

AC = AB + BC
AC = (72x + 25) + (216x + 50)
AC = 72x + 25 + 216x + 50
AC = 288x + 75

Therefore, the lengths of AB, BC, and AC are:

AB = 72x + 25
BC = 216x + 50
AC = 288x + 75