Answer:
[tex]\large\boxed{x=\dfrac{2b+7}{a-b}}[/tex]
Step-by-step explanation:
[tex]ax-7=b(x+2)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\ax-7=bx+2b\qquad\text{add 7 to both sides}\\\\ax=bx+2b+7\qquad\text{subtract}\ bx\ \text{from both sides}\\\\ax-bx=2b+7\\\\(a-b)x=2b+7\qquad\text{divide both sides by}\ (a-b)\neq0\\\\x=\dfrac{2b+7}{a-b}[/tex]