Answer:
[tex]\large\boxed{x=\dfrac{9}{4}=2\dfrac{1}{4}}[/tex]
Step-by-step explanation:
[tex]-9(x-5)=x+22\dfrac{1}{2}\qquad\text{multiply both sides by 2}\\\\(2)(-9)(x-5)=2x+(2)\left(22\dfrac{1}{2}\right)\\\\-18(x-5)=2x+45\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\(-18)(x)+(-18)(-5)=2x+45\\\\-18x+90=2x+45\qquad\text{subtract 90 from both sides}\\\\-18x+90-90=2x+45-90\\\\-18x=2x-45\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\-18x-2x=2x-2x-45\\\\-20x=-45\qquad\text{divide both sides by (-20)}\\\\\dfrac{-20x}{-20}=\dfrac{-45}{-20}\\\\x=\dfrac{45:5}{20:5}\\\\x=\dfrac{9}{4}\to x=2\dfrac{1}{4}[/tex]
