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The distributive property is a fundamental concept in algebra. It states that multiplying a single term by terms inside a parenthesized expression is the same as multiplying the term by each part of the parenthesized expression and then adding or subtracting the results. Here's how it applies to our exercise.

Take the original inequality: 3(u-1) - 3(u+1) < 2. The distributive property tells us that we need to multiply 3 by each term inside the parentheses. This changes the inequality to: 3 * u - 3 * 1 - 3 * u - 3 * 1 < 2. Simplifying inside the parentheses further makes it: 3u - 3 - 3u - 3 < 2. So, the use of the distributive property transforms the initial complex expression into a simpler one that we can work with more easily.

Simplifying algebraic expressions involves reducing complexity without changing the expression's meaning. After using the distributive property in our exercise, we see that we need to simplify the expression further: 3u - 3 - 3u - 3. Notice that we have like terms, so the expression simplifies to: 3u - 3u - 3 - 3. Here, the terms involving u cancel out each other: 3u - 3u = 0. This leaves us with: -6 < 2. To simplify algebraic expressions efficiently, always follow these steps:

• Apply the distributive property where necessary.
• Combine like terms.
• Reduce the equation to its simplest form.

Properly simplifying expressions makes solving algebraic problems more manageable and clearer.

Combining like terms is crucial when simplifying algebraic expressions. Like terms are terms that have the same variables raised to the same power. For example, in our inequality: 3u - 3 - 3u - 3 < 2. The terms 3u and -3u are like terms. They both have the variable u with an exponent of 1. When we combine these terms: 3u - 3u. The result is 0 because any number minus itself is zero. Thus, the expression simplifies further: -3 - 3 = -6. Now, our inequality looks like: -6 < 2. By combining like terms, you reduce the number of terms in the expression, making it simpler and easier to solve.