Problem 54 - Beginning and Intermediate Algebra

Question

Simplify each expression. \(r-6-12 r-4+16\)

Step-by-Step Solution

Answer

-12r + 6

Step 1: Combine Like Terms

Identify and combine the like terms in the expression. Like terms are those terms that have the same variable raised to the same power. In this expression, we have the terms involving 'r' and the constant terms. So we group them together: Terms involving 'r': -12r Constants:-6, -4, +16

Step 2: Combine Constant Terms

Add all the constant terms together: -6 - 4 + 16 First, -6 - 4 = -10 Then, -10 + 16 = 6

Step 3: Combine All Terms

Now combine the simplified like terms together: -12r (from step 1) + 6 (from step 2) The simplified expression is: -12r + 6

Key Concepts

combining like terms

Understanding how to combine like terms is crucial when simplifying algebraic expressions. Like terms are terms that have the same variable raised to the same power. For instance, in the expression \(r - 6 - 12r - 4 + 16\), the like terms involving 'r' are \r\ and \-12r\. Similarly, the constants in this expression are \-6\, \-4\, and \+16\. To combine like terms, group the terms with the same variable together and then perform the operations. This step helps in reducing the complexity of the expression and makes it easier to work with.

constants in algebra

Constants in algebra are terms without variables. They remain fixed and do not change value. In the expression \(r - 6 - 12r - 4 + 16\), the constants are \-6\, \-4\, and \+16\. To simplify algebraic expressions, you will often need to combine these constants. Start by adding or subtracting them as indicated. For example, in this case, \-6 - 4\ results in \-10\, and then \-10 + 16\ gives us \+6\. This simplified approach ensures a clear and concise final expression.

algebraic simplification

Algebraic simplification is the process of rewriting an expression in a simpler form. This usually involves combining like terms and simplifying constants. Here's a breakdown of how this is done using our expression \(r - 6 - 12r - 4 + 16\):

• First, identify and group the like terms. Here, \-12r\ is the only term involving 'r', and the constants are \-6\, \-4\, and \+16\.
• Next, simplify the constants: Combine \-6\ and \-4\ to get \-10\, then add \+16\ to get \+6\.
• Finally, combine all the simplified terms: \-12r + 6\.

This results in the simplified expression \-12r + 6\. Simplification makes it easier to handle algebraic expressions, particularly when solving equations or performing further operations.