8.6 数字线上的不平等-interactive

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• 选择节数字行的不平等

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  数字行的不平等

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  Quantum Cold
  ::量冷

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  A quantum computer is a special type of computer that uses quantum mechanics to perform computations at incredibly fast speeds. This type of computing has the potential to revolutionize medicine, data science, and many other fields. In order to take advantage of the quantum properties which allow a quantum computer to run , the computer must be kept at a temperature of -459.7°F or lower.
  ::量子计算机是一种特殊类型的计算机,它使用量子力学以令人难以置信的快速速度进行计算。 此类计算机有可能使医学、数据科学和许多其他领域发生革命性的变化。 为了利用允许量子计算机运行的量子属性,计算机必须保持在-459.7°F或更低的温度。

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  T he temperatures at which  a quantum computer would function can be represented using a number line.  Use the interactive below to identify where possible values for these temperatures lie on the number line and practice writing an inequality to represent the situation.
  ::使用数字线代表量子计算机运行的温度。 使用下面的交互线来确定这些温度的可能值, 数值线在数字线上, 并练习写出不平等来代表情况 。

  

  INTERACTIVE

  Quantum Cold

  

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  • Drag the red points onto the number line at temperatures the computer could run.
    ::在计算机可以运行的温度下,将红色点拖到数字线上。
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  • Use the dropdown menu and input box to enter the expression that represents temperatures the computer can run.
    
    ::使用下拉菜单和输入框输入代表计算机可运行温度的表达式。

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  What can you say about the possible temperatures of the computer according to the inequality and number line?
  ::根据不平等和数字线 计算机的温度如何?

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  There are more possibilities for the temperature of the computer than you can count.
  ::计算机温度的可能性比你能计算到的要大。

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  There are not many possible temperatures.
  ::可能气温不多。

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  Inequalities on the Number Line
  ::数字行的不平等

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  As  you saw in the previous activity, an inequality involving a variable can represent an amount of infinite numbers. To show these values, highlight the side of the line represented by the inequality. The highlighted part of the graph represents an infinite number of points.
  ::正如您在上一个活动中所看到的那样,一个变量所涉及的不平等可以代表无限数字。要显示这些数值,请突出显示不平等代表的线的侧面。图中突出显示的部分代表无限的点数。

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  In the following interactive, create your own inequality and observe how there are many points that can satisfy the inequality.
  ::在接下来的互动中,创造你自己的不平等,并观察有多少点可以满足不平等。

  

  INTERACTIVE

  Inequalities on a Number Line

  

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  • Use the drop down menu and red point to create an inequality.
    ::使用下调菜单和红点来造成不平等。
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  • Click the button to graph the inequality on a number line.
    ::单击该按钮以图形显示数字行上的不平等。

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  Think about the graph of $\begin{align*}-3\ge x.\end{align*}$
  ::想想- 3x 的图形 。

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  Select the true statements.
  ::选择真实语句。

  Select all that apply

  a 播放段落

  There will be a closed circle on -3.
  ::将在 - 3 上有一个封闭的圆圈。

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  The number line will be shaded to the left of -3.
  ::数字行将在 - 3 左侧阴影下。

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  There will be an open circle on -3.
  ::在 - 3 上将有一个开放的圆圈。

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  The number line will be shaded to the right of -3.
  ::数字行将依右 - 3 的阴影进行。

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  To show an inequality that is greater than or less than ( but not equal to) a number, use an open circle .
  ::要显示大于或小于(但不等于)数字的不平等,请使用开放圆。

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  To show an inequality that is 'greater than or equal to' or 'less than or equal to'  a number, use a  closed circle.
  ::要显示“ 大于或等于” 或“ 小于或等于” 数字的不平等, 请使用闭环 。

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  Example
  ::示例示例示例示例

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  Graph  the inequality  $\begin{array}{r}x\ge 7\frac{1}{2}\end{array}$  on a number line.
  ::在数字行上图解不平等 x712 。

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  This inequality states that  $\begin{array}{r}x\end{array}$  is a number that is greater than or equal to  $\begin{array}{r}7\frac{1}{2}.\end{array}$  The values represented by this inequality are  $\begin{array}{r}7\frac{1}{2},8,8\frac{1}{3},9,9\frac{3}{4}...\end{array}$  and every other number  greater than  $\begin{array}{r}7\frac{1}{2}.\end{array}$
  
  ::这种不平等表明x是一个大于或等于712的数值,这种不平等所代表的数值为712,818,813,939,934...,其他数值均大于712。

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  Because the inequality includes   $\begin{array}{r}7\frac{1}{2},\end{array}$  as you can see from the  $\begin{array}{r}\ge \end{array}$  sign, draw  a closed circle  at  $\begin{array}{r}7\frac{1}{2}\end{array}$ before shading the values  above  (to the right of)  $\begin{array}{r}7\frac{1}{2}.\end{array}$  
  ::因为不平等包括 712, 正如您从“ ” 符号中看到的那样, 在阴影以上( 右侧) 712 值之前, 请在 712 处画一个封闭的圆圈 。

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  Answer: 
  ::答复:

  

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  Example
  ::示例示例示例示例

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  Show the inequality  $\begin{array}{r}x<2.8\end{array}$  on a number line.
  ::在数字行中显示不平等 x<2.8 。

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  This inequality states that  $\begin{array}{r}x\end{array}$  is a number less than 2.8. The values represented by this inequality are 2.7, 2, 1, 0, -1... and every other value less than 2.8.
  ::这种不平等表明x的数值小于2.8。 这种不平等所代表的数值是2.7、2、1、0、-1.,其他数值小于2.8。

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  Because the inequality  excludes  2.8, as you can see from the $\begin{array}{r}<\end{array}$  sign, draw an  open circle at 2.8 before shading the values below (to the left of) 2.8.
  ::因为不平等排除了2.8, 从 < 符号中可以看到, 在将2.8以下( 向左) 的数值涂黑之前, 画一个2.8 的开放圆圈 。

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  Answer:
  ::答复:

  

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  Writing Inequalities
  ::写作不平等

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  In the interactive below, you will practice completing inequality statements based on a given number line or matching the number line to a given inequality.
  ::在下文互动中,您将实践根据特定数字行填写不平等声明,或将数字行与特定不平等匹配。

  

  INTERACTIVE

  Writing Inequalities

  

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  • Select the number line or inequality statement that corresponds to the inequality or number line given at the top.
    ::选择与顶部给出的不平等或数字行相对应的数字行或不平等语句。
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  • Press the "Check" button to check your answer.
    ::按“ 检查” 按钮检查您的回答 。

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   Summary
  ::摘要

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  • Inequalities with a variable can represent infinite numbers.
    ::与变量的不平等可以代表无限数字。
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  • A number line can be used to show all the possible values of an inequality.
    ::数字行可用于显示不平等的所有可能值。
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  • To graph an inequality on a number line, follow these rules (where $\begin{array}{r}n\end{array}$  is  a number):
    ::在数字线上绘制不平等图时,遵循这些规则(n是数字):

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  $$\begin{array}{r}\begin{array}{|ccc|}\hline & \text{open circle}& \text{closed circle}\\ \text{to the left}& x<n& x\le n\\ \text{to the right}& x>n& x\ge n\\ \hline\end{array}\end{array}$$

  
  ::左下角的开放圆圈圆形,右下角为 <nx\n>nx\n