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Chapter 1: Problem 93

Simplify. $$ 8 x-(6 x+7) $$

Short Answer

Expert verified
2x - 7

Step by step solution

01

Distribute the Negative Sign

Distribute the negative sign across the terms inside the parenthesis. This involves multiplying each term inside the parenthesis by -1. The expression becomes: 8x - 6x - 7
02

Combine Like Terms

Combine the like terms, which are the terms with the variable x. Add or subtract the coefficients of x:i.e., 8x - 6x = 2x
03

Write the Simplified Expression

After combining the like terms, write the simplified expression. The final simplified form is:2x - 7

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Key Concepts

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

Distribute Negative Sign
The first step in simplifying the expression is to distribute the negative sign through the parentheses. When you see a negative sign in front of a parenthesis, it means you should multiply each term inside by -1. This step changes the signs of the terms within the parenthesis.
For example, in the expression \(8x - (6x + 7)\), you need to apply the negative sign to both \(6x\) and \(7\).
  • \(-6x\) instead of \(6x\)
  • \(-7\) instead of \(+7\)
Thus, the expression becomes \(8x - 6x - 7\).
Distributing the negative sign is crucial because it ensures that every term is accurately represented before moving on to the next step.
Combine Like Terms
The next step involves combining like terms. Like terms are terms that have the same variable raised to the same power. In our example, the like terms are \(8x\) and \(-6x\).
To combine these like terms, simply add or subtract their coefficients (the numerical part attached to the variable).
  • \(8x - 6x = 2x\)
Combining like terms simplifies the expression because it reduces the number of terms you have to deal with. In this case, we are left with \(2x - 7\).
Simplified Expression
After distributing the negative sign and combining like terms, you're now ready to write the simplified expression. This is the final, most straightforward form of the expression.
Our example is simplified to \(2x - 7\). This expression is easier to work with than the original because it has fewer terms and no parenthesis.
To recap, simplifying an algebraic expression involves:
  • Distributing any negative signs.
  • Combining like terms.
  • Writing the resulting simplified expression.
This makes complex algebraic expressions easier to understand and manage.

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