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Chapter 5: Problem 176

Simplify each expression. $$ 7 x-(5+5 x)+3 $$

Short Answer

Expert verified
2x - 5

Step by step solution

01

- Distribute Negative Sign in Parentheses

Identify and distribute the negative sign inside the parentheses to both terms: 7x - (5 + 5x) becomes 7x - 5 - 5x.
02

- Combine Like Terms

Combine the like terms (terms with the same variable): 7x - 5x - 5. This combines to (7x - 5x) - 5 which simplifies further to 2x - 5.

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Key Concepts

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

Distributing Negative Signs
When you encounter parentheses in an algebraic expression, especially with a negative sign in front of it, it鈥檚 essential to distribute the negative sign to each term inside the parentheses. For example, in the expression \(7x - (5 + 5x)\), the negative sign in front of the parentheses will change the signs of the terms inside. This turns \(+5\) into \(-5\) and \(+5x\) into \(-5x\), resulting in the expression becoming \(7x - 5 - 5x\).
Remember:
  • A negative sign before parentheses inverts the signs of all terms within the parentheses.
  • This is equivalent to multiplying both terms inside by \(-1\).
Combining Like Terms
Next, after distributing any negative signs, you need to combine like terms. Like terms are terms that have the same variable raised to the same power. For instance, in the simplified expression \(7x - 5 - 5x\), notice that both \(7x\) and \(-5x\) are like terms because they both contain the variable \(x\).
Combine these terms by performing the relevant addition or subtraction: \(7x - 5x\). This results in \(2x\).
  • Always look for terms with the same variables.
  • If they are raised to the same power, group them together.
  • Combine them by performing the necessary addition or subtraction.
Intermediate Algebra
Intermediate algebra involves operations that are foundational for higher-level math. It focuses on manipulating algebraic expressions, including distributing signs and combining like terms, as seen in the previous sections. To successfully master intermediate algebra:
  • Practice distributing signs, especially negative ones.
  • Get comfortable identifying and combining like terms.
  • Work on simplifying complex expressions step-by-step.

Remember: Practice is key for mastering these concepts. Don鈥檛 rush through steps and ensure you understand each process thoroughly before moving on.

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Most popular questions from this chapter

Write each number in standard notation. $$ -6 \times 10^{4} $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \left(z^{-4} x^{3}\right)^{-1} $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ 4^{4} \cdot 4^{-6} $$

Evaluate. Express answers in standard notation. $$ \frac{3 \times 10^{-2}}{12 \times 10^{3}} $$

Simplify each expression so that no negative exponents appear in the final result. Assume that all variables represent nonzero real numbers. $$ \frac{\left(3 r^{2}\right)^{2} r^{-5}}{r^{-2} r^{3}}\left(2 r^{-6}\right)^{2} $$
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