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Combining like terms means adding or subtracting terms that have the same variable raised to the same power. It is a crucial step in simplifying algebraic expressions. When working with an expression like

• \((3x - 4) + (9x - 1)\)

look for terms that share common characteristics.
In this case, the terms \(3x\) and \(9x\) are like terms because they both involve the variable \(x\) raised to the first power. Similarly, the constants \(-4\) and \(-1\) are like terms.
Combining like terms involves performing the operation (addition or subtraction) on their coefficients. For example, adding the coefficients of \(3x\) and \(9x\) gives you \(12x\), and subtracting the constants \(-4\) and \(-1\) results in \(-5\). This simplifies our expression significantly, making future operations easier and more straightforward.

Simplifying expressions means making the expression as concise as possible by performing all possible operations and combining like terms. This process helps in understanding the expression better and solving it in a more efficient way. When you simplify the expression

• \((3x - 4) + (9x - 1)\),

you start by looking out for any like terms.
Combine them as discussed earlier:
\[ 3x + 9x = 12x \]and\[-4 - 1 = -5\].
Thus, the simplified expression becomes \(12x - 5\).

• This form is easier to work with and provides clarity, paving the way for solving equations or performing further mathematical operations.

By following a few basic steps, you can take any complex expression and transform it into something simplified and manageable.

The distributive property is a valuable tool in algebra that involves multiplying a single term by terms inside parentheses. Although it might not seem necessary in our specific exercise of \((3x - 4) + (9x - 1)\), it's still an essential concept to grasp.
The principle indicates that when you have an expression of the form \(a(b + c)\), you can distribute \(a\) to both \(b\) and \(c\). This produces the expression \(ab + ac\).

• This rule allows you to eliminate parentheses and simplify expressions further.

Understanding the distributive property makes it easier to handle more complex expressions and equations in algebra.
While our example does not require the distributive property, knowing when and how to apply it to other problems is critical for success in algebra.