text: Alg_Complete
  
  # That is the meaning of the above the equal sign in
  
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  Unformatted text preview: ill start off this chapter with a fairly short section with some basic terminology that we use on a fairly regular basis in solving equations and inequalities. First, a solution to an equation or inequality is any number that, when plugged into the equation/inequality, will satisfy the equation/inequality. So, just what do we mean by satisfy? Let’s work an example or two to illustrate this. Example 1 Show that each of the following numbers are solutions to the given equation or inequality. (a) x = 3 in x 2 - 9 = 0 [Solution] (b) y = 8 in 3 ( y + 1) = 4 y - 5 [Solution] (c) z = 1 in 2 ( z - 5 ) £ 4 z [Solution] (d) z = -5 in 2 ( z - 5 ) £ 4 z [Solution] Solution (a) We first plug the proposed solution into the equation. ? 32 - 9 = 0 9-9 = 0 0=0 OK So, what we are asking here is does the right side equal the left side after we plug in the proposed solution. That is the meaning of the “?” above the equal sign in the first line. Since the right side and the left side are the same we say that x = 3 satis...
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  ## This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
  
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explanation: The provided text is an excerpt from a document that appears to be a chapter or section from a mathematics textbook or course material. The text introduces the concept of solutions to equations and inequalities and provides an example with multiple parts (a, b, c, d) to illustrate the idea of a solution satisfying an equation or inequality. Each part of the example is labeled as a "Solution" and includes a step-by-step verification of whether the given number is a solution.
  
  The text contains a question and an answer, specifically in the form of an example with a detailed solution.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Alg_Complete
  
  # That is the meaning of the above the equal sign in
  
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  Unformatted text preview: ill start off this chapter with a fairly short section with some basic terminology that we use on a fairly regular basis in solving equations and inequalities. First, a solution to an equation or inequality is any number that, when plugged into the equation/inequality, will satisfy the equation/inequality. So, just what do we mean by satisfy? Let’s work an example or two to illustrate this. Example 1 Show that each of the following numbers are solutions to the given equation or inequality. (a) x = 3 in x 2 - 9 = 0 [Solution] (b) y = 8 in 3 ( y + 1) = 4 y - 5 [Solution] (c) z = 1 in 2 ( z - 5 ) £ 4 z [Solution] (d) z = -5 in 2 ( z - 5 ) £ 4 z [Solution] Solution (a) We first plug the proposed solution into the equation. ? 32 - 9 = 0 9-9 = 0 0=0 OK So, what we are asking here is does the right side equal the left side after we plug in the proposed solution. That is the meaning of the “?” above the equal sign in the first line. Since the right side and the left side are the same we say that x = 3 satis...
  View Full Document
  
  ## This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
  
  Ask a homework question - tutors are online
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is an excerpt from a document that appears to be a chapter or section from a mathematics textbook or course material. The text introduces the concept of solutions to equations and inequalities and provides an example with multiple parts (a, b, c, d) to illustrate the idea of a solution satisfying an equation or inequality. Each part of the example is labeled as a "Solution" and includes a step-by-step verification of whether the given number is a solution.
  
  The text contains a question and an answer, specifically in the form of an example with a detailed solution.
  
  Label: question-and-answer