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When you solve an equation, the goal is to find the value of the unknown variable. This process often starts with isolating the variable on one side of the equation. Think of the equation as a balance scale. What you do to one side, you must also do to the other side to keep things balanced. For instance, in the given problem, we start with the equation: \[4 - 3d = 5d - 4\] To isolate the terms with the variable \(d\) on one side, you can add \(3d\) to both sides, resulting in: \[4 = 8d - 4\] Notice how we move all terms involving \(d\) to one side of the equation. This is the cornerstone of solving equations: isolating the variable. Make sure to move terms in a way that keeps the equation balanced!

Basic algebra involves understanding how to manipulate equations with the goal of finding the value of an unknown variable. Key operations include addition, subtraction, multiplication, and division. In the step-by-step solution of the exercise, we've seen these operations in action: - **Addition**: Adding \(3d\) to both sides.- **Subtraction**: Moving terms around by essentially subtracting or adding them to both sides. After isolating the variable with addition, we simplify the equation to: \[4 = 8d - 4\] Next, we perform an addition operation to move the constant terms together. By adding 4 to both sides, we get: \[8 = 8d\] Finally, we solve for \(d\) by dividing both sides by 8.

Solving an equation is like following a recipe. Here are the key steps to follow: 1. **Combine like terms**: If there are any, combine them to simplify the equation. 2. **Isolate the variable**: Move terms with the variable to one side and constants to the other. 3. **Simplify**: Reduce the equation to its simplest form by basic arithmetic operations.4. **Solve**: Lastly, isolate the variable by performing the necessary operations. In our example, we first isolated the variable terms: \[4 = 8d - 4\] We then isolated the constant terms: \[8 = 8d\] Finally, we solved for \(d\) by dividing both sides by 8, leading to: \[d = 1\] Remember, mastering these equation solving steps can make any algebra problem more manageable and less intimidating!