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Chapter 5: Problem 37

Subtract. $$ (7 x+4)-(2 x+1) $$

Short Answer

Expert verified
5x + 3

Step by step solution

01

- Distribute the negative sign

Remove the parentheses by distributing the negative sign through the second set of terms: ewline (7x + 4) - (2x + 1) = 7x + 4 - 2x - 1.
02

- Group like terms

By grouping the like terms, we get: ewline (7x - 2x) + (4 - 1).
03

- Simplify

Simplify the expression by performing the subtraction: ewline 5x + 3.

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Key Concepts

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

Distributive Property
The distributive property is a fundamental algebraic principle. It states that multiplying a sum by a number is the same as doing each multiplication separately. Here's how it works: if you have a negative sign outside of parentheses, you distribute it to each term inside. For example, in the problem (7x + 4) - (2x + 1), the negative sign must be applied to both 2x and 1. This changes the problem to 7x + 4 - 2x - 1. By distributing the negative sign, you can remove the parentheses and work with individual terms.
Combining Like Terms
Combining like terms is essential for simplifying algebraic expressions. Like terms have the same variable part. For instance, in the expression 7x + 4 - 2x - 1, the terms 7x and -2x are like terms because they both have the variable x. To combine them, you simply add or subtract their coefficients: 7x - 2x = 5x. The constants 4 and -1 are also combined: 4 - 1 = 3. Combining these gives us a simplified expression: 5x + 3.
Simplifying Expressions
Simplifying an expression means making it as simple as possible. This is done by:
  • Distributing any coefficients or signs
  • Combining like terms
Let's walk through the original problem. First, we distribute the negative sign: (7x + 4) - (2x + 1) becomes 7x + 4 - 2x - 1. Next, we combine like terms. The like terms are 7x and -2x, which combine to 5x. The constants 4 and -1 combine to 3. This gives us the simplified expression: 5x + 3. By following these steps鈥攄istribute, combine like terms, and simplify鈥攜ou'll be able to solve similar problems more easily.

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Most popular questions from this chapter

Using the window \([-5,5,-1,9],\) graph \(y_{1}=5\) \(y_{2}=x+2,\) and \(y_{3}=\sqrt{x} .\) Then predict what shape the graphs of \(y_{1}+y_{2}, y_{1}+y_{3},\) and \(y_{2}+y_{3}\) will take. Use a graph to check each prediction.

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