Q. 51 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 51–56, solve for x,

$\left|\begin{array}{ll}x& x\\ 4& 3\end{array}\right|=5$

Step-by-Step Solution

Answer

The value of x is $-5$.

Step 1. Given Information

We are given, 

$\left|\begin{array}{ll}x& x\\ 4& 3\end{array}\right|=5$

We have to find the value of x.

Step 2. Solving the determinant

Solving the determinant, we get

$$\begin{gathered} \left|\begin{array}{ll}x& x\\ 4& 3\end{array}\right|=5 \\ \left(x\right) 3-4\left(x\right)=5 \\ 3 x-4 x=5 \\ -x=5 \\ x=-5 \end{gathered}$$

Hence, the value of x is $-5$.