Solve the linear equation (−1/2) · (x − 5) + 3 = −5/2 and find the exact value of x.

Introduction / Context:

This algebra question requires solving a simple linear equation that involves a fractional coefficient and a bracket. It tests your ability to distribute a negative fraction, combine like terms, and isolate the variable x. Such equations appear frequently in aptitude tests and form a foundation for more advanced algebra.

Given Data / Assumptions:

• The equation is (−1/2) · (x − 5) + 3 = −5/2.
• x is a real number.
• Standard arithmetic operations and distribution rules apply.
• The goal is to find the unique value of x that satisfies the equation.

Concept / Approach:

We first distribute the factor −1/2 across the bracket (x − 5). Then we combine the resulting terms with the constant 3 on the left side. After that, we move constants to one side and keep the x term on the other side. Multiplying by −2 at the right point clears the fraction and makes solving straightforward.

Step-by-Step Solution:

Verification / Alternative check:

Substitute x = 16 back into the original equation. Compute x − 5 = 16 − 5 = 11. Then (−1/2) * 11 = −11/2. Add 3, which is 6/2, to get −11/2 + 6/2 = −5/2, which matches the right side. This confirms that x = 16 satisfies the equation exactly.

Why Other Options Are Wrong:

Substituting 4, −6, −4, or 6 into the equation does not produce −5/2 on the left side. These incorrect values usually result from errors in distributing the minus sign or combining the fractional terms. Only x = 16 gives the required equality.

Common Pitfalls:

Learners often forget that multiplying a negative fraction by a negative number gives a positive term. Others may try to multiply by 2 too early and misplace signs. Carefully distributing and converting integers to fractions with a common denominator greatly reduces the chance of mistakes.

Final Answer:

The solution of the equation (−1/2)(x − 5) + 3 = −5/2 is x = 16.