Answer
$x=18$.
Work Step by Step
The given equation is
$\Rightarrow \frac{3}{2}(x-2)-5=19$
Use distributive property.
$\Rightarrow \frac{3}{2}x-3-5=19$
Combine like terms.
$\Rightarrow \frac{3}{2}x-8=19$
Add $8$ to each side.
$\Rightarrow \frac{3}{2}x-8+8=19+8$
Simplify.
$\Rightarrow \frac{3}{2}x=27$
Multiply each side by $\frac{2}{3}$.
$\Rightarrow \frac{2}{3}\cdot \frac{3}{2}x=\frac{2}{3}\cdot 27$
Simplify.
$\Rightarrow x=18$
Check:-
$\Rightarrow \frac{3}{2}(18-2)-5=19$
$\Rightarrow \frac{3}{2}(16)-5=19$
$\Rightarrow 24-5=19$
$\Rightarrow 19=19$
True.
Hence, the solution is $x=18$.
