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Understanding how to simplify algebraic expressions is crucial in algebra. You often encounter expressions with variables and constants grouped together. Simplifying them involves a few systematic steps to make the expression easier to work with or solve.
The expression given in the exercise is: i(4(x + 3) - 8(x - 7)) At first, this may look complex, but don't worry; we will break it down into simpler parts using the distributive property and combine like terms.
By simplifying algebraic expressions, you learn how to manipulate mathematical symbols. This skill is important for solving equations and understanding higher-level mathematics. Keep practicing to build a strong foundation!

Combining like terms is a straightforward yet vital step in simplifying algebraic expressions. Like terms are terms that contain the same variables raised to the same power. In our example, the like terms are the ones with the variable x. Here's an overview of how we handle them.
From the step-by-step solution:
1. First, we distributed the numbers: 4(x + 3) - 8(x - 7) = 4x + 12 - 8x + 56
2. Next, we identify like terms. In this case, 4x and -8x are like terms because they both contain the variable x.
Combining these, we get:4x - 8x + 12 + 56
Notice that the constants (12 and 56) are also considered like terms. After combining: -4x + 68.
Combining like terms helps make the expression much simpler and easier to interpret. The key is to carefully identify terms with the same variables and then sum or subtract their coefficients.

Prealgebra lays the foundation for all future math courses. It includes basic concepts that you need to understand before moving on to more advanced topics like algebra and calculus. Prealgebra exercises often involve tasks like distributing, combining like terms, and simplifying expressions, just as we did in the given problem.
Let’s recap the process with the given exercise example:
1. Distribute the coefficients: 4(x + 3) - 8(x - 7)
2. This gives: 4x + 12 - 8x + 56
3. Combine the like terms: 4x - 8x + 12 + 56
4. Finally, simplified: -4x + 68.

Through these exercises, you build core skills in arithmetic, fractions, and basic equations. Practice regularly to get comfortable with each step. This practice helps ensure you are well-prepared as you advance to higher levels of math.