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Chapter 5: Problem 31

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

Short Answer

Expert verified
5x + 3

Step by step solution

01

- Distribute the Negative Sign

Rewrite the subtraction expression by distributing the negative sign to each term inside the parentheses. This changes the expression to (7x + 4) - 2x - 1.
02

- Group Like Terms

Group the like terms together. Combine the terms with x and the constant terms separately: (7x - 2x) + (4 - 1).
03

- Simplify

Simplify by performing the arithmetic on the grouped terms: 7x - 2x = 5x and 4 - 1 = 3. The expression becomes 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 allows us to distribute a single term across terms inside parentheses. In algebraic subtraction such as (7x + 4) - (2x + 1), we apply this property by ensuring every term inside the parentheses is appropriately addressed.
For example:
- (2x + 1) = -2x - 1
This step helps us turn a complex expression into something manageable, by eliminating the parentheses.
Like Terms
Once the parentheses are removed, the next step is to group like terms together. Like terms are terms that have the same variable raised to the same power.
In our example, after distributing the negative sign, we have: (7x + 4) - 2x - 1
Here, 7x and -2x are like terms because they both contain the variable x. Similarly, 4 and -1 are constants and can be grouped together.
  • 7x - 2x
  • 4 - 1
Grouping like terms makes it easier to simplify the expression in the next step.
Simplifying Expressions
The final step involves simplifying the expression by combining the like terms. This means to perform the arithmetic operations on the grouped terms.
For the terms involving variables: 7x - 2x = 5x
For the constants: 4 - 1 = 3
So, the simplified version of our original expression will be: 5x + 3
Simplifying expressions help us reach the most compact and understandable form of an algebraic equation. It is essential for solving and analyzing equations efficiently.

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Most popular questions from this chapter

Add or subtract, as indicated. $$ \left(5 a^{2} b+7 a b\right)+\left(9 a^{2} b-5 a b\right)+\left(a^{2} b-6 a b\right) $$

For each pair of functions fand \(g\), determine the domain of the sum, the difference, and the product of the two functions. $$ \begin{aligned} &f(x)=x+\frac{2}{x-1}\\\ &g(x)=3 x^{3} \end{aligned} $$

Convert to scientific notation. $$ 0.00583 $$

Express using positive exponents and, if possible, simplify. $$5 a^{-7} b^{4}$$

Subtract. $$ \begin{aligned} &\begin{array}{r} {5 x^{4}-2 x^{3}+6 x^{2}} \\ {-\left(7 x^{4} \quad+7 x^{2}\right)} \\ \hline \end{array}\\\ &= \end{aligned} $$
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