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Chapter 1: Problem 7

Simplify each expression. $$ 5+2(x-3 y) $$

Short Answer

Expert verified
5 + 2x - 6y

Step by step solution

01

- Distribute

Distribute the 2 through the parentheses: 5 + 2(x - 3y) = 5 + 2x - 6y
02

- Simplify

Combine like terms: 5 + 2x - 6y

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Key Concepts

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

Distribution
When you're simplifying algebraic expressions, one of the first things you often do is distribution. Distribution means you'll multiply a single term outside the parentheses by each term inside the parentheses.

In the exercise given, we're distributing the 2 across (x - 3y).
  • Start by multiplying 2 by x to get 2x
  • Next, multiply 2 by -3y to get -6y
So, after distribution, the expression 5 + 2(x - 3y) transforms into 5 + 2x - 6y.
This step helps break down expressions and makes combining like terms easier in the next step.
Combining Like Terms
After distribution, the next step is to simplify the expression by combining like terms. 'Like terms' are terms whose variables (and their exponents) are the same.

In our exercise, once we've distributed 2 to get 5 + 2x - 6y, we need to look for like terms to combine.
However, in this example, we have different terms:
  • Constant term: 5
  • Variable term with x: 2x
  • Variable term with y: -6y
In this case, there are no like terms to combine since they all have different variables or are constants. Hence, the expression remains 5 + 2x - 6y.
Combining like terms simplifies expressions and makes them easier to work with in further algebraic operations.
Algebraic Simplification
Algebraic simplification involves making an expression as simple as possible. It's like cleaning up your workspace, removing unnecessary complexity.

The main steps in algebraic simplification are:
  • Distribution: Multiply terms to remove parentheses
  • Combining like terms: Group and simplify terms with the same variables
In our example, we started with the expression 5 + 2(x - 3y).
After applying distribution and combining like terms, we simplified it to: 5 + 2x - 6y.
Simplifying expressions is essential for solving equations and understanding algebra well. It makes it easier to see relationships between terms and to perform further operations on the expressions.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. The sum of \(-18\) and \(-6,\) divided by the product of 2 and \(-4\)

Write a numerical expression for each phrase and simplify. The quotient of \(-20\) and the sum of \(-8\) and \(-2\)

Simplify each expression. $$ -4(5 y-7)+3(2 y-5) $$

Perform each indicated operation. $$ \frac{-13(-4)-(-8)(-2)}{(-10)(2)-4(-2)} $$

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