1. The problem is to find the value of $x$ in the equation $$\frac{2x+3}{5} = 7.$$\n\n2. The formula used here is to solve linear equations by isolating the variable $x$.\n\n3. First, multiply both sides of the equation by 5 to eliminate the denominator:\n$$5 \times \frac{2x+3}{5} = 5 \times 7$$\nwhich simplifies to\n$$2x + 3 = 35.$$\n\n4. Next, subtract 3 from both sides to isolate the term with $x$:\n$$2x + 3 - 3 = 35 - 3$$\nwhich simplifies to\n$$2x = 32.$$\n\n5. Finally, divide both sides by 2 to solve for $x$:\n$$x = \frac{32}{2} = 16.$$\n\n6. Therefore, the solution to the equation is $x = 16$.