#### Answer

conditional equation;
solution: $x=\frac{3}{2}$

#### Work Step by Step

Distribute 4 on the left side and distribute 5 on the right side to obtain:
$4x-12+5=x+5x-10$
Simplify each side of the equation by combining like terms:
$4x-7=6x-10$
Subtract $4x$ on both sides of the equation to obtain:
$-7=2x-10$
Add 10 on both sides of the equation to obtain:
$3=2x$
Divide $2$ on both sides of the equation to obtain:
$\frac{3}{2}=x$
The given equation has $x=\frac{3}{2}$ as a solution therefore it is a conditional equation.