# if $$\begin{bmatrix} x+2 & 3 \\ x+5 & 4 \end{bmatrix}=3,$$ find the value of x.

Toolbox:
• If $A=\begin{bmatrix}a_{11} & a_{12}\\a_{21} & a_{22}\end{bmatrix}$then,
• |A|=$a_{11}\times a_{22}-a_{12}\times a_{21}$
Given:

$\begin{vmatrix}x+2 & 3\\x+5 & 4\end{vmatrix}$=3.

On expanding we get,

$\Delta=4(x+2)-3(x+5)=3.$

$\Rightarrow 4x+8-3x-15=3.$

$\Rightarrow x-7=3.$

$\Rightarrow x=10.$

Hence x=10.