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Chapter 1: Problem 49

Simplify each expression. $$ 16-5 m-4 m-2+2 m $$

Short Answer

Expert verified
The simplified expression is 14 - 7m.

Step by step solution

01

- Identify Like Terms

Recognize the terms involving the variable and the constant terms. In this expression, the like terms are those involving the variable 'm' and the constant numbers.
02

- Group Like Terms

Group all the like terms together. The given expression is: 16 - 5m - 4m - 2 + 2m Group the like terms to get: (16 - 2) + (-5m - 4m + 2m).
03

- Combine Like Terms

First, combine the constant terms: 16 - 2 = 14 Then, combine the terms with 'm': -5m - 4m + 2m = (-5 - 4 + 2)m = -7m So the simplified expression is: 14 - 7m.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Like Terms
Understanding 'like terms' is fundamental when simplifying algebraic expressions.
Like terms are terms that have identical variable parts raised to the same power.
For instance, in the expression given, 16 - 5m - 4m - 2 + 2m, the terms involving 'm' are the like terms.
These like terms include -5m, -4m, and 2m because they all have the variable 'm'.
The other terms, like 16 and -2, are constant terms and are also considered like terms without the variables.
Grouping Like Terms
Once you've identified the like terms, the next step is to group them together.
This makes it easier to perform the necessary operations to combine them.
In our example, we start with the expression: 16 - 5m - 4m - 2 + 2m.
Group the constant terms together and the 'm' terms together.
This modifies the expression to (16 - 2) + (-5m - 4m + 2m).
Grouping like terms is simply a way to organize the expression so the next steps are more straightforward.
Combining Like Terms
After grouping like terms, combine them by performing the arithmetic operations.
For constants: 16 - 2 = 14.
For the terms with 'm': -5m - 4m + 2m.
First, add the coefficients (numbers in front of the variables): -5, -4, and 2.
This gives you: -5 - 4 + 2 = -7.
Then, multiply by the variable 'm' to get -7m.
So, the expression reduces to 14 - 7m.
Algebra Simplification Steps
Simplifying algebraic expressions involves a few clear steps.
Start by identifying the like terms, both constants and variable terms, in the given expression.
Next, group these like terms to organize your expression.
Then, combine the grouped like terms by performing the necessary arithmetic operations.
Finally, rewrite the expression with the simplified terms.
In the exercise, we followed these steps to simplify 16 - 5m - 4m - 2 + 2m to 14 - 7m.
By consistently applying these steps, you can simplify any algebraic expression efficiently.

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