Final answer:
To solve for x, we can use the midpoint formula to find the values of B and D. Then, we substitute these values into the given expression and solve for x by simplifying the equation and isolating the variable. The solution for x is 5/3 or approximately 1.67.
Step-by-step explanation:
To solve for x, we can use the midpoint formula B = (A + C)/2 and D = (C + E)/2.
Given that B is the midpoint of AC, we have B = (A + C)/2. Rearranging the equation, we get 2B = A + C. Similarly, D is the midpoint of CE, so D = (C + E)/2. Rearranging the equation, we get 2D = C + E.
Substituting the equations for B and D into the expression BD - 5x + 3, we get (2B - 5x + 3) - 5x + 3. Simplifying, we have 2B - 10x + 6 - 5x + 3 = 0. Combining like terms, we get 2B - 15x + 9 = 0.
Now we can substitute the given values for B and A into the equation and solve for x. Let's say B = 8 and A = 4x + 18. Substituting these values into the equation, we have 2(8) - 15x + 9 = 0. Simplifying, we get 16 - 15x + 9 = 0. Combining like terms, we have -15x + 25 = 0. Subtracting 25 from both sides, we get -15x = -25. Dividing both sides by -15, we get x = 25/15. Simplifying, we get x = 5/3 or x = 1.67.