ACT Math Practice Question #1206 (Hard (35)) | Test Citadel
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ACT Math Difficulty: Hard (35)

Digital ACT Math Practice Question #1206

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

Given the $2 \times 2$ matrix $M = \begin{bmatrix} x & 3 \\ 4 & x - 1 \end{bmatrix}$, for what positive value of $x$ is the determinant of $M$ equal to $8$?
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Test Choice A ($x = 5$): $\det = 5(4) - 3(4) = 20 - 12 = 8$. Match found on the first try!

Masterclass Solution & Distractor Trap Analysis

The determinant of a $2 \times 2$ matrix $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$ is $ad - bc$. $$\det(M) = x(x - 1) - (3)(4) = x^2 - x - 12.$$ Set the determinant equal to $8$: $$x^2 - x - 12 = 8 \implies x^2 - x - 20 = 0.$$ Factorin...

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

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