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Chapter 5: Problem 38

Subtract. $$ (5 x+6)-(2 x+4) $$

Short Answer

Expert verified
3x + 2

Step by step solution

01

Distribute the Minus Sign

Rewrite the expression by distributing the minus sign to each term in the parentheses: (5x + 6) - (2x + 4) = 5x + 6 - 2x - 4
02

Combine Like Terms

Group and combine the like terms: For the terms with x: 5x - 2x = 3x For the constant terms: 6 - 4 = 2
03

Write the Final Expression

Combine the simplified terms to get the final expression: 3x + 2

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Key Concepts

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

distributing minus sign
When you see a subtraction operation in algebra, you might have to distribute a minus sign across multiple terms inside parentheses. For example, in the expression (5x + 6) - (2x + 4), the minus sign before the second parentheses affects both terms within. This is how it works:
  • You change the sign of each term inside the parentheses that follow the minus sign.
  • The expression in parentheses (2x + 4) becomes (-2x - 4).
It is important to distribute the minus sign correctly to ensure you subtract each term properly. After distributing, the equation changes to:(5x + 6) - (2x + 4) = 5x + 6 - 2x - 4.
combining like terms
Once you have distributed the minus sign, the next step is to combine like terms. Like terms have the same variables raised to the same power. For example, 5x and -2x are like terms because both terms have the variable x. In the expression 5x + 6 - 2x - 4, you can combine the terms as follows:
  • Group the terms with x: 5x - 2x = 3x.
  • Group the constant terms: 6 - 4 = 2.
Combining like terms simplifies the expression. Always make sure each term is properly combined with its like counterpart.
simplifying expressions
After distributing the minus sign and combining like terms, the final step is to simplify the expression. Simplifying means to reduce the expression to its simplest form. In our example, the expression has been reduced to: 3x + 2. This is the most concise version of the original expression. Simplifying makes it easier to interpret and solve more complex equations.
  • Ensure there are no like terms left to combine.
  • Ensure all operations, like distributing and combining, have been correctly applied.
By following these steps, you can confidently simplify any algebraic expression.

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