SAT Math Practice Question #769 (Hard (800)) | Test Citadel
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SAT Math Difficulty: Hard (800)

Digital SAT Math Practice Question #769

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

The absolute value inequality \( |kx - 12| \le c \) has a solution set of \( -2 \le x \le 8 \), where \( k \) and \( c \) are positive constants. What is the value of \( k + c \)?
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Socratic AI Engine Step-by-Step Derivation
0ms Precomputed
Tactical Insight (Hint 1)

A system of equations represents geometric intersections. Consider substitution, elimination, or setting both expressions equal.

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

Absolute value inequalities that yield a bounded range require a strong foundational understanding of how bounds are constructed. Let's deconstruct the inequality mechanically. Step 1: Remove the absolute value. The expression \( |kx - 12| ...

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

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