QuestionJuly 15, 2025

Solve the equation for x vert } 4x&x 9x vert =28 The solution set is square (Simplify your answer. Use a comma to separate answers as needed.)

Solve the equation for x vert } 4x&x 9x vert =28 The solution set is square (Simplify your answer. Use a comma to separate answers as needed.)
Solve the equation for x vert } 4x&x 9x vert =28 The solution set is square (Simplify your answer. Use a comma to separate answers as needed.)

Solution
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Answer

The solution set is \{\} (empty set). Explanation 1. Calculate the Determinant The determinant of a 2x2 matrix \begin{pmatrix} a & b \\ c & d \end{pmatrix} is given by **ad - bc**. Here, a = 4x, b = x, c = 9x, and d = 0. So, the determinant is 4x \cdot 0 - x \cdot 9x = -9x^2. 2. Set the Determinant Equal to 28 Solve -9x^2 = 28 for x. This gives x^2 = -\frac{28}{9}. 3. Analyze the Solution Since x^2 cannot be negative in real numbers, there are no real solutions.

Explanation

1. Calculate the Determinant<br /> The determinant of a 2x2 matrix $\begin{pmatrix} a & b \\ c & d \end{pmatrix}$ is given by **$ad - bc$**. Here, $a = 4x$, $b = x$, $c = 9x$, and $d = 0$. So, the determinant is $4x \cdot 0 - x \cdot 9x = -9x^2$.<br /><br />2. Set the Determinant Equal to 28<br /> Solve $-9x^2 = 28$ for $x$. This gives $x^2 = -\frac{28}{9}$.<br /><br />3. Analyze the Solution<br /> Since $x^2$ cannot be negative in real numbers, there are no real solutions.
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