Find X if B is the midpoint of AC, AB=18 and AC=10x-4

X = 4

4.4 To find the value of x, we need to use the fact that "B is the midpoint of AC."

In a given line segment, the midpoint divides the segment into two equal parts. Therefore, we can set up an equation using this information.

Since B is the midpoint of AC, we know that AB is equal to BC. It means that AB + BC is equal to AC.

So, using the values we have, we can write the equation as follows:

AB + BC = AC

Given that AB is 18 and AC is 10x-4, we can substitute these values into the equation:

18 + BC = 10x - 4

To solve for BC, we need to isolate it on one side of the equation. Firstly, let's move the constant term to the other side:

BC = 10x - 4 - 18

Simplifying further:

BC = 10x - 22

Now we can substitute this value of BC back into the equation and solve for x:

18 + (10x - 22) = 10x - 4

Simplifying the equation:

18 + 10x - 22 = 10x - 4

Combine like terms:

10x - 4 = 10x - 4

Subtract 10x from both sides:

-4 = -4

Since both sides of the equation are equal, the value of x can be any real number. The equation is true regardless of the value of x.

Therefore, x can be any real number.