SAT Math Practice Question #307 (Hard (785)) | Test Citadel
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SAT Math Difficulty: Hard (785)

Digital SAT Math Practice Question #307

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

The equation below is true for all \( x eq \frac{3}{a} \): \[ \frac{2x^2 + bx + c}{ax - 3} = -4x + 5 + \frac{R}{ax - 3} \] where \( a \), \( b \), \( c \), and \( R \) are constants. What is the value of \( 2b + 4a \)?
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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)

Desmos Tactical Shortcut: Plot the left-hand side and right-hand side as separate equations (e.g. \( y_1 = f(x) \) and \( y_2 = g(x) \)). Click the intersection points directly to read exact coordinates.

Masterclass Solution & Distractor Trap Analysis

The SAT loves testing your ability to manipulate rational expressions. When a problem states that an equation is 'true for all \( x \)' (except where the denominator is zero), it means we are dealing with an identity. The polynomials on bot...

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

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