1. The problem is to find the value of $x$ in the equation $$\frac{2x+3}{5} = 7.$$ 2. The formula used here is to isolate $x$ by eliminating the denominator and then solving the resulting linear equation. 3. Multiply both sides of the equation by 5 to get rid of the denominator: $$2x + 3 = 7 \times 5$$ 4. Simplify the right side: $$2x + 3 = 35$$ 5. Subtract 3 from both sides to isolate the term with $x$: $$2x = 35 - 3$$ $$2x = 32$$ 6. Divide both sides by 2 to solve for $x$: $$x = \frac{32}{2}$$ $$x = 16$$ 7. Therefore, the solution to the equation is $x = 16$.