# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/2

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Problem 2

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## Exercise 2

### Question

export const metadata = {
  title: "Problem 2",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

The value of <InlineMath math="x" /> that satisfies the following equation is ...

<MathContainer>
  <BlockMath math="\begin{vmatrix} -6 & 3 \\ 2 & 4 \end{vmatrix} = \begin{vmatrix} 2x & 3 \\ -4x & -1 \end{vmatrix}" />
</MathContainer>


### Choices

- [ ] $$\frac{15}{2}$$
- [ ] $$\frac{9}{7}$$
- [ ] $$\frac{5}{2}$$
- [ ] $$-2$$
- [x] $$-3$$

### Answer & Explanation

export const metadata = {
    title: "Solution to Problem 2",
    authors: [{ name: "Nabil Akbarazzima Fatih" }],
    date: "12/23/2025",
};

We are given a determinant equation of <InlineMath math="2 \times 2" /> matrices. Recall that the formula for the determinant of a matrix <InlineMath math="\begin{vmatrix} a & b \\ c & d \end{vmatrix}" /> is <InlineMath math="ad - bc" />.

#### Calculating the Left Hand Side Determinant

First, we calculate the determinant of the matrix on the left side:

<MathContainer>
  <BlockMath math="\begin{vmatrix} -6 & 3 \\ 2 & 4 \end{vmatrix} = (-6)(4) - (3)(2)" />
  <BlockMath math="= -24 - 6" />
  <BlockMath math="= -30" />
</MathContainer>

#### Calculating the Right Hand Side Determinant

Next, we calculate the determinant of the matrix on the right side which contains the variable <InlineMath math="x" />:

<MathContainer>
  <BlockMath math="\begin{vmatrix} 2x & 3 \\ -4x & -1 \end{vmatrix} = (2x)(-1) - (3)(-4x)" />
  <BlockMath math="= -2x - (-12x)" />
  <BlockMath math="= -2x + 12x" />
  <BlockMath math="= 10x" />
</MathContainer>

#### Determining the Variable Value

Now we equate both determinant results according to the original equation:

<MathContainer>
  <BlockMath math="-30 = 10x" />
</MathContainer>

Divide both sides by 10 to find the value of <InlineMath math="x" />:

<MathContainer>
  <BlockMath math="x = \frac{-30}{10}" />
  <BlockMath math="x = -3" />
</MathContainer>

Thus, the value of <InlineMath math="x" /> that satisfies the equation is -3.


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