To find the value of x, we need to solve the mean equation and simplify it step by step.

Given data:
2x + 3, x + 4, 5x + 10, -4x + 5, x + 3 with a mean of 55.

Step 1: Find the sum of all the terms
The sum of the terms is (2x + 3) + (x + 4) + (5x + 10) + (-4x + 5) + (x + 3).

Step 2: Simplify the equation by combining like terms
Combine the x terms and the constant terms separately:
(2x + x + 5x - 4x + x) + (3 + 4 + 10 + 5 + 3) = 13x + 25.

Step 3: Set up the mean equation
The mean equation is (sum of the terms) / (number of terms) = mean.

In this case, the mean equation is (13x + 25) / 5 = 55.

Step 4: Solve the equation for x
Multiply both sides of the equation by 5 to eliminate the denominator:
13x + 25 = 55 * 5
13x + 25 = 275

Subtract 25 from both sides of the equation:
13x = 275 - 25
13x = 250

Divide both sides of the equation by 13 to solve for x:
x = 250 / 13
x ≈ 19.23

Therefore, the value of x is approximately 19.23.

Explanation:
- We start by finding the sum of all the given terms.
- Then, we simplify the equation by combining like terms.
- Next, we set up the mean equation and substitute the sum of the terms into it.
- Finally, we solve the equation for x by performing the necessary algebraic operations.

By following these steps, we find that the value of x is approximately 19.23.

X=5/2