Question

When proving the statement below, what is the long-term goal? If 3r−8=10, then r=6.

Answer 1

The long-term goal is to prove that the given equation is true by manipulating it and deriving the value of r that satisfies it.

Step-by-step explanation:

The long-term goal of proving the statement 'If 3r-8=10, then r=6' is to show that the equation is true for all values of r that satisfy it. In order to prove this, we need to use logical reasoning and mathematical operations to manipulate the equation and derive the value of r that makes the equation true.

Here is the step-by-step process:

1. Start with the given equation: 3r-8=10
2. Add 8 to both sides to isolate the term with r: 3r-8+8=10+8
3. Simplify the equation: 3r=18
4. Divide both sides of the equation by 3 to solve for r: 3r/3 = 18/3
5. Final step: r = 6