Solve the linear equation 5x - (1/2)(2x - 7) = 5.5 (that is, 11/2) by simplifying both sides and isolating x, then choose the correct value of x from the options.

Introduction / Context:
This is a straightforward linear equation involving a fraction and a bracketed expression. Such problems are very common in aptitude tests and are designed to see if you can correctly expand and simplify expressions with fractions. Once the equation is simplified, you can solve for x in a few clear steps and then match the result with the given options.

Given Data / Assumptions:

• The equation is 5x - (1/2)(2x - 7) = 5.5.
• 5.5 can be written as 11/2 to work with exact fractions.
• x is a real number.
• Standard algebraic rules apply when expanding brackets and combining like terms.

Concept / Approach:
First, rewrite 5.5 as 11/2 to keep everything in fractional form. Then expand the bracket (1/2)(2x - 7) to simplify the left hand side. After combining like terms, you will have a simple linear equation in x. Solving it involves isolating x on one side of the equation by basic operations such as addition and division.

Step-by-Step Solution:
Rewrite the equation with fractions: 5x - (1/2)(2x - 7) = 11/2. Expand the bracket: (1/2)(2x - 7) = x - 7/2. Substitute into the equation: 5x - (x - 7/2) = 11/2. Distribute the minus sign: 5x - x + 7/2 = 11/2. Combine x terms: 4x + 7/2 = 11/2. Isolate 4x by subtracting 7/2 from both sides: 4x = 11/2 - 7/2 = 4/2 = 2. Divide both sides by 4: x = 2 / 4 = 1/2.
Verification / Alternative check:
Substitute x = 1/2 back into the original equation. Compute 2x - 7 = 2*(1/2) - 7 = 1 - 7 = -6. Then (1/2)(2x - 7) = (1/2)*(-6) = -3. The left hand side becomes 5x - (1/2)(2x - 7) = 5*(1/2) - (-3) = 5/2 + 3 = 5/2 + 6/2 = 11/2, which equals 5.5. This confirms that x = 1/2 satisfies the equation exactly.

Why Other Options Are Wrong:
Option b (3/2), option c (-1/2), option d (-3/2), and option e (-5/2) do not satisfy the equation when substituted back, and they arise from typical algebraic mistakes such as forgetting to distribute the minus sign, miscomputing 11/2 - 7/2, or mishandling the division by 4. Only x = 1/2 makes both sides of the equation equal.

Common Pitfalls:
A common error is to expand (1/2)(2x - 7) incorrectly as (2x/2 - 7) or to forget the negative sign in front of the entire bracket. Another pitfall is to convert 5.5 incorrectly into a fraction or to mix decimals and fractions, leading to unnecessary complexity. Working consistently in fractions and checking each step for sign accuracy helps avoid these issues.

Final Answer:
The correct solution of the equation 5x - (1/2)(2x - 7) = 5.5 is x = 1/2.