Problem 49 - Algebra 1: Concepts and Skills

Question

Simplify the expression. $$2 k-8-8 k$$

Step-by-Step Solution

Answer

-6k - 8

Step 1: Identify like terms

The like terms in the given expression (2k - 8 - 8k) are 2k and -8k. The term 8 is a constant and cannot be combined with the like terms.

Step 2: Combine like terms

To combine the like terms, add the coefficients of both terms together. That is, add the coefficient of 2k (which is 2) to the coefficient of -8k (which is -8). This gives you -6k.

Step 3: Rewrite the expression with the simplified like terms

After combining the like terms, the expression 2k - 8 - 8k simplifies to -6k - 8.

Key Concepts

Simplifying Expressions

Simplifying expressions means rewriting them in a simpler or more efficient form. In algebra, this often involves cleaning up terms to make the expression less cluttered and easier to work with. When simplifying expressions, always look for "like terms." These are terms in the expression that have the same variable raised to the same power. You can only combine like terms. In the expression \(2k - 8 - 8k\), the terms \(2k\) and \(-8k\) are like terms because they both contain the variable \(k\). By combining them, we simplify the expression, removing unnecessary complexity. Use simple addition or subtraction of coefficients to simplify like terms.

Algebraic Expressions

An algebraic expression is a mathematical phrase that can involve numbers, variables, and operators (like addition and subtraction, etc.). Unlike equations, algebraic expressions do not have an equality sign (such as \(=\)).It’s important to identify which parts of an expression can be simplified and which cannot. For example:

• In \(2k - 8 - 8k\), \(2k\) and \(-8k\) are variable terms, and
• \(-8\) is a constant term.

These parts work together to build the structure of the expression. Understanding how to manage each component helps in working with algebraic expressions effectively.

Coefficients

Coefficients are the numbers that appear in front of the variables in algebraic expressions. They indicate how many of each variable you have. Coefficients are critical when you are performing operations such as combining like terms.Look at the expression \(2k - 8 - 8k\) again. Here, \(2\) and \(-8\) are the coefficients of terms \(2k\) and \(-8k\), respectively. They tell us that there are 2 units of \(k\) and \(-8\) units of \(k\), which, when combined, result in \(-6k\).Understanding and identifying coefficients correctly allow you to combine like terms effectively, thus simplifying the expression. The operation between coefficients is basic arithmetic, like adding 2 and \(-8\) to get \(-6\). This process enables you to rewrite expressions in a simpler form.