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Chapter 2: Problem 17

Translate from algebraic notation to words. \(y-1>6\)

Short Answer

Expert verified
One less than the number is greater than six.

Step by step solution

01

Identify Components

Recognize the parts of the inequality: the variable, the constant terms, and the inequality symbol.
02

Translate Variable

Translate the variable 'y' as 'a number'.
03

Translate Constant

Translate the constant term '-1' as 'one less than the number'.
04

Convert Inequality Symbol

Recognize that the '>' symbol means 'is greater than'.
05

Combine and Formulate

Combine all translated components. 'One less than the number is greater than six.'

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Key Concepts

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

Inequalities in Mathematics
Inequalities in mathematics are statements that compare two values or expressions. Instead of showing exactly how much one value equals another, inequalities tell us about the relative size of one value compared to another. Inequalities use symbols like '<', '>', '鈮�', and '鈮�'.
For example:
  • '<' means 'less than'.
  • '>' means 'greater than'.
  • '鈮�' means 'less than or equal to'.
  • '鈮�' means 'greater than or equal to'.
In our specific exercise, we deal with an inequality that looks like this: (y - 1 > 6). This tells us that 'y' minus one is greater than six. Understanding these symbols is the first step in being able to translate these mathematical statements into words or vice versa.
Algebraic Notation
Algebraic notation is the method of writing mathematical expressions using variables, constants, and symbols. It allows us to generalize mathematical statements and solve problems more abstractly. For example, the expression: y - 1 > 6 is written in algebraic notation. Here's a breakdown of the components:
  • 'y' is a variable that can represent any number.
  • '-1' is a constant, a fixed number subtracted from 'y'.
  • '>' is an inequality symbol that means 'greater than'.
Using this notation makes it easier to formulate and solve equations and inequalities systematically. In our exercise, this algebraic notation (y - 1 > 6) has been translated into a sentence: 'One less than the number is greater than six.'
Mathematical Translation
Mathematical translation involves converting equations, expressions, and inequalities from symbols to words or vice versa. This skill is essential for understanding and solving word problems. Here's how we translate (y - 1 > 6):Let's break it down:
  • 'y' is translated to 'a number'.
  • '-1' becomes 'one less'.
When we put it all together with the inequality symbol '>', which means 'greater than', we get: 'One less than the number is greater than six'.
The process of this translation helps students recognize and interpret mathematical symbols in everyday language, making it an essential skill in algebra and beyond.

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Most popular questions from this chapter

In the following exercises, evaluate each expression. $$ 8 x-3 \text { when } x=4 $$

In the following exercises, find the least common multiple of each pair of numbers. $$ 25,35 $$

In the following exercises, simplify, using the order of operations. $$ 4+3 \cdot 5 $$

In the following exercises, solve each equation using the subtraction property of equality. $$ p+18=23 $$

In the following exercises, translate the given sentence into an algebraic equation. The sum of eight times x and 4 is 68.
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