SAT Math Practice Question #789 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #789

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

How many integers \( x \) satisfy the inequality \[ |x^2 - 12x + 20| \le -x^2 + 12x - 20 \]?
Select Your Answer:
Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

Identify the quadratic form: consider converting to vertex form \( y = a(x-h)^2 + k \) or using \( x = - rac{b}{2a} \) to find the line of symmetry.

Elimination Framework (Hint 2)

Elimination Shortcut: Check the extremes or test answer choices starting with C to binary search the correct magnitude.

Masterclass Solution & Distractor Trap Analysis

This problem looks terrifying, but it unlocks beautifully if you understand the absolute definition of absolute value. Step 1: Simplify visually by substitution. Let's define a single variable to represent the quadratic expression. Let \( E...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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