If (36 − 16x) − (4x − 8) = 4, solve the equation step by step and find the exact value of x. Be careful with the minus sign before the second bracket while simplifying.

Introduction / Context: This is a straightforward linear-equation simplification problem, but it tests a very common trap: subtracting a bracketed expression. When you have (A) - (B), every term inside B changes sign. If you forget to flip the signs, you will get the wrong coefficient of x and the wrong constant. Once simplified correctly, the equation becomes a single-variable linear equation that can be solved in one or two steps.

Given Data / Assumptions:

• Equation: (36 - 16x) - (4x - 8) = 4 • Required: value of x

Concept / Approach: Distribute the minus sign across the second bracket: -(4x - 8) = -4x + 8. Then combine like terms (x terms and constants) and solve the resulting linear equation by isolating x.

Step-by-Step Solution: 1) Start: (36 - 16x) - (4x - 8) = 4 2) Distribute the minus sign into the second bracket: 36 - 16x - 4x + 8 = 4 3) Combine constants: 36 + 8 = 44 4) Combine x terms: -16x - 4x = -20x 5) So the equation becomes: 44 - 20x = 4 6) Subtract 44 from both sides: -20x = 4 - 44 = -40 7) Divide by -20: x = (-40)/(-20) = 2

Verification / Alternative check: Substitute x = 2: LHS = (36 - 16*2) - (4*2 - 8) = (36 - 32) - (8 - 8) = 4 - 0 = 4. RHS = 4. Both sides match, so x = 2 is correct.

Why Other Options Are Wrong: • 3, 4, 6, -2: result from sign mistakes when opening the bracket or from incorrect combining of -16x and -4x.

Common Pitfalls: • Writing -(4x - 8) as -4x - 8 (wrong; the -8 becomes +8). • Combining constants incorrectly: 36 and 8 must add to 44.

Final Answer: 2