Solve the equation for x.
-$$\left| \begin{array} { r r }
- 2 & 5 \
1 & x
\end{array} \right| = - 7$$
A) $\{ 1 \}$
B) $\{ - 7 \}$
C) $\{ 6 \}$
D) $\varnothing$

Question

Solve the equation for x.
-$$\left| \begin{array} { r r } 
- 2 & 5 \
1 & x
\end{array} \right| = - 7$$
A) $\{ 1 \}$
B) $\{ - 7 \}$
C) $\{ 6 \}$
D) $\varnothing$

Quizplus · Accepted Answer

The determinant of a 2x2 matrix is calculated as $ad - bc$. Here, $a = -2$, $b = 5$, $c = 1$, and $d = x$. So, the determinant is $(-2)x - (5)(1) = -2x - 5$. Setting this equal to -7 gives $-2x - 5 = -7$. Solving for $x$, we add 5 to both sides to get $-2x = -2$, and then divide by -2 to find $x = 1$.

Solve the Equation for X ∣−251x∣=−7\left| \begin{array} { r r } - 2 & 5 \\1 & x\end{array} \right| = - 7​−21​5x​​=−7

Solve the Equation for X $\left| \begin{array} { r r } - 2 & 5 \\1 & x\end{array} \right| = - 7$