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Chapter 1: Problem 87

Write an equivalent expression without using grouping symbols. $$ -[5-6 x] $$

Short Answer

Expert verified
-5 + 6x

Step by step solution

01

- Identify the expression inside the grouping symbols

The expression inside the grouping symbols is \(5 - 6x\).
02

- Apply the distribution of the negative sign

Distribute the negative sign across the terms inside the brackets. This means multiplying each term inside the brackets by -1: \[ -[5 - 6x] = -1 \times 5 + (-1) \times (-6x) \]
03

- Simplify the expression

Simplify the result from Step 2: \[ -1 \times 5 + (-1) \times (-6x) = -5 + 6x \]

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Key Concepts

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

Equivalent Expressions
In algebra, equivalent expressions are different expressions that represent the same value. For instance, if you distribute a negative sign across the terms within a parenthesis, you are creating an equivalent expression. Consider the original expression from the exercise:
  • Original: \( -[5 - 6x] \)
  • Equivalent: \( -5 + 6x \)
This transformation involves applying the negative sign to each term inside the brackets, resulting in a new expression that has the same value as the original one for any value of \(x\). Understanding equivalent expressions helps in simplifying and solving equations.
Simplifying Algebraic Expressions
Simplifying algebraic expressions involves reducing them to their simplest form. This makes it easier to solve or analyze an expression. Take the expression given in the exercise:
  • Expression: \( -[5 - 6x] \)
  • Step: Apply the negative sign to each term within the brackets.
By distributing the negative sign, we transform \( 5 \) into \( -5 \) and \( -6x \) into \(+6x\). This simplifies our expression to \( -5 + 6x \). Simplifying helps in better understanding and solving algebraic equations.
Algebraic Operations
Algebraic operations are the foundation of solving problems in algebra. They include addition, subtraction, multiplication, and division. In the exercise, the main operation used was distributing a negative sign through multiplication:
  • Taking \( -1 \) (the negative sign) and multiplying it by \( 5 \).
  • Taking \( -1 \) and multiplying it by \(-6x\).
This process converts \( 5 \) to \( -5 \) and \(-6x\) to \(+6x\), demonstrating how multiplication is key to distributing negative signs in algebraic expressions.

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Most popular questions from this chapter

Given that \(0.3 \overline{3}=\frac{1}{3}\) and \(0.6 \overline{6}=\frac{2}{3},\) express each of the following as a ratio of two integers. $$0.9 \overline{9}$$

Evaluate. $$ 50 \div 2 \cdot t, \text { for } t=-5 $$

Simplify. $$ 4 a-b-4(5 a-7 b+8 c) $$

Simplify. Match the algebraic expression with the equivalent rewritten expression below. Check your answer by calculating the expression by hand and by using a calculator. A) \((5(3-7)+4 \wedge 3) /(-2-3)^{2}\) B) \((5(3-7)+4 \wedge 3) /\left(-2-3^{2}\right)\) C)\((5(3-7)+4) \wedge 3 /-2-3^{2}\) D) \(5(3-7)+4 \wedge 3 /(-2-3)^{2}\) $$ \frac{5(3-7)+4^{3}}{(-2-3)^{2}} $$

List in order from least to greatest. $$-\frac{2}{3}, \frac{1}{2},-\frac{3}{4},-\frac{5}{6}, \frac{3}{8}, \frac{1}{6}$$
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