Final answer:
To solve the equation 3/4 r + 20 = 29, we subtract 20 from both sides and then multiply both sides by the reciprocal of 3/4 to find r = 12. For the equation x + 20 = 29, we subtract 20 from both sides to find x = 9. Other examples demonstrate solving proportions and quadratic equations.
Step-by-step explanation:
To solve the equation 3/4 r + 20 = 29, we need to perform algebraic operations to isolate the variable r. First, we will subtract 20 from both sides of the equations to get 3/4 r = 9. Next, we will multiply both sides of the equation by the reciprocal of 3/4, which is 4/3, to find the value of r. By doing this, we get r = (9 * 4/3), which simplifies to r = 12.
A different approach is required for the equation x + 20 = 29. Here, we simply subtract 20 from both sides to find that x = 9.
In the other examples provided, the use of algebraic rearrangement, setting up proportions, cross-multiplying, and applying the quadratic formula are demonstrated as methods for solving equations or finding unknown quantities. The specific details of these methods depend on the form and parameters of each equation.