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Chapter 2: Problem 100

For exercises 97-100, simplify. $$ 9 x-(3 x-8) $$

Short Answer

Expert verified
6x + 8

Step by step solution

01

Distribute the negative sign

Begin by distributing the negative sign across the terms inside the parentheses. This changes \(9x - (3x - 8)\) to \(9x - 3x + 8\).
02

Combine like terms

Next, combine the like terms. The terms involving \(x\) are 9x and -3x. Combine them: \( (9x - 3x + 8) \). This becomes \(6x + 8\).

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Key Concepts

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

Distributive Property
When simplifying algebraic expressions, the distributive property is a powerful tool. This property allows you to simplify expressions by distributing a factor across terms inside parentheses. For example, in the expression \(9x - (3x - 8)\), the negative sign needs to be applied to both terms inside the parentheses.

Here鈥檚 how it works:
  • Identify the terms inside the parentheses: \(3x - 8\)
  • Distribute the negative sign to both terms: \(-3x + 8\)
  • Re-write the expression: \(9x - 3x + 8\)

The expression is now simpler and ready for the next step, which involves combining like terms.
Combining Like Terms
Once you've distributed any factors or signs, the next step is to combine like terms. Like terms are terms that have the same variables raised to the same power. In our example, the terms \(9x\) and \(-3x\) are like terms because they both involve the variable \(x\).

Here are the steps:
  • Identify the like terms: \(9x\) and \(-3x\)
  • Combine them: \(9x - 3x = 6x\)

By combining these like terms, the expression reduces to \(6x + 8\). This makes the algebraic expression much simpler and easier to handle.

Combining like terms helps to eliminate redundancy and simplifies calculations. It is a crucial step in algebraic simplification.
Algebraic Simplification
Algebraic simplification involves a series of steps aimed at rewriting an expression in a simpler or more manageable form. Simplifying expressions makes it easier to work with them, especially in more complex equations.

Here are the general steps involved in algebraic simplification:
  • Use the distributive property to remove parentheses.
  • Combine like terms to reduce the number of terms in the expression.
  • Rearrange the expression, if necessary, to make it more readable.

Taking our example \(9x - (3x - 8)\) through these steps, we get:\(9x - 3x + 8 = 6x + 8\).

The result \(6x + 8\) is the simplified form of the original expression. This simplified version is easier to work with and understand in solving further algebraic problems. Remember, practice makes perfect. Keep practicing these steps until they become second nature!

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Most popular questions from this chapter

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