Simplify the expression:
$2(3x + 4) - (10x + 8)$
The objective is to simplify the algebraic expression \(2(3x + 4) - (10x + 8)\). This expression consists of variables and constants combined through addition, subtraction, and multiplication. We will use the distributive property and the rules of combining like terms to simplify it.
First, we apply the distributive property to the first term \(2(3x + 4)\). Multiplying 2 by each term inside the parentheses, we get:
\[2(3x) + 2(4) = 6x + 8\]
Next, we handle the second part of the expression, \(-(10x + 8)\). This is equivalent to multiplying the terms inside the parentheses by -1:
\[-(10x + 8) = -10x - 8\]
Now, we combine the simplified parts into one expression:
\[(6x + 8) - 10x - 8\]
Grouping the like terms (the terms with \(x\) and the constant terms), we obtain:
\[(6x - 10x) + (8 - 8)\]
Simplifying each group:
\[(6 - 10)x + 0 = -4x\]
Thus, the simplified form of the expression is \(\boxed{-4x}\).
Understanding how to simplify algebraic expressions is a foundational skill in many fields. For example, in budgeting or inventory management, you might track costs or quantities using variables. If you have an initial budget represented by an expression and need to subtract various expenses (also represented as expressions), simplifying the resulting expression helps you quickly calculate the net amount or remaining resources. Mastering these operations allows you to manipulate and interpret data more efficiently in real-world scenarios.